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Sequences and Series Objective Questions for UP TGT Exam

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Sequences and Series Objective Questions for UP TGT

Sequences and Series Objective Questions for UP TGT Exam

1. The first term of an arithmetic sequence is 5, and the common difference is 3. What is the 10th term?

a) 32

b) 29

c) 35

d) 38

2. In a geometric sequence, the first term is 2, and the common ratio is 3. What is the 5th term?

a) 54

b) 162

c) 108

d) 81

3. The sum of the first 10 terms of an arithmetic sequence is 100, and the first term is 1. What is the common difference?

a) 2

b) 3

c) 1

d) 4

4. Which term of the arithmetic sequence 7, 10, 13, … is 40?

a) 12th

b) 11th

c) 13th

d) 14th

5. The sum of an infinite geometric series is 12, and the first term is 8. What is the common ratio?

a) 1/3

b) 2/3

c) 1/2

d) 3/4

6. In an arithmetic sequence, the 5th term is 23, and the 10th term is 38. What is the first term?

a) 7

b) 8

c) 9

d) 10

7. The first three terms of a geometric sequence are 4, 12, 36. What is the 6th term?

a) 324

b) 972

c) 108

d) 2916

8. The sum of the first 6 terms of an arithmetic sequence is 87, and the first term is 2. What is the common difference?

a) 5

b) 4

c) 3

d) 6

9. In a harmonic sequence, the 3rd term is 1/5, and the 6th term is 1/11. What is the 1st term?

a) 1/3

b) 1/2

c) 1/4

d) 1/6

10. The 4th term of an arithmetic sequence is 13, and the 7th term is 22. What is the 1st term?

a) 4

b) 5

c) 6

d) 7

11. The sum of the first 8 terms of a geometric series is 255, and the common ratio is 2. What is the first term?

a) 1

b) 2

c) 3

d) 4

12. What is the sum of the first 12 terms of the arithmetic sequence whose 3rd term is 7 and 7th term is 15?

a) 180

b) 192

c) 204

d) 216

13. In a geometric sequence, the 2nd term is 6, and the 4th term is 24. What is the common ratio?

a) 2

b) 3

c) 4

d) 6

14. The first term of an AP is 3, and the 10th term is 39. What is the sum of first 10 terms?

a) 210

b) 220

c) 230

d) 240

15. The sum of an infinite geometric series is 20, and the first term is 15. What is the common ratio?

a) 1/4

b) 1/3

c) 1/5

d) 1/4

16. In an arithmetic sequence, the 3rd term is 10, and the 8th term is 25. What is the 15th term?

a) 40

b) 45

c) 50

d) 55

17. The first three terms of a geometric sequence are 3, 6, 12. What is the sum of the first 5 terms?

a) 60

b) 63

c) 93

d) 48

18. The sum of the first 5 terms of an arithmetic sequence is 65, and the first term is 5. What is the common difference?

a) 4

b) 5

c) 6

d) 7

19. In a harmonic sequence, the 2nd term is 1/8, and the 5th term is 1/20. What is the 4th term?

a) 1/12

b) 1/14

c) 1/16

d) 1/18

20. The 6th term of an arithmetic sequence is 17, and the 11th term is 32. What is the 20th term?

a) 59

b) 62

c) 65

d) 68

21. In a geometric sequence, the 3rd term is 16, and the 6th term is 128. What is the first term?

a) 2

b) 4

c) 8

d) 16

22. The sum of the first 9 terms of an arithmetic sequence is 171, and the first term is 3. What is the common difference?

a) 4

b) 5

c) 6

d) 7

23. The first term of a geometric series is 5, and the common ratio is 1/2. What is the sum of the infinite series?

a) 8

b) 10

c) 12

d) 15

24. In an arithmetic sequence, the 2nd term is 7, and the 6th term is 19. What is the 10th term?

a) 31

b) 29

c) 33

d) 35

25. The sum of the first 7 terms of a geometric sequence is 127, and the common ratio is 2. What is the first term?

a) 1

b) 2

c) 3

d) 4

26. The 4th term of a geometric sequence is 1/27, and the common ratio is 1/2. What is the first term?

a) 1/3

b) 1/9

c) 1/6

d) 1/12

27. In an arithmetic sequence, the sum of the first 10 terms is 250, and the first term is 10. What is the common difference?

a) 4

b) 5

c) 6

d) 7

28. The first three terms of an arithmetic sequence are 8, 14, 20. What is the sum of the first 15 terms?

a) 570

b) 580

c) 590

d) 600

29. The sum of an infinite geometric series is 18, and the first term is 12. What is the common ratio?

a) 1/3

b) 1/2

c) 2/3

d) 3/4

30. In an arithmetic sequence, the 7th term is 29, and the 12th term is 49. What is the first term?

a) 1

b) 2

p)c) 3

d) 4

31. The 2nd term of a geometric sequence is 6, and the 5th term is 48. What is the 7th term?

a) 192

b) 384

c) 96

d) 768

32. The sum of the first 6 terms of an arithmetic sequence is 72, and the first term is 2. What is the common difference?

a) 3

b) 4

c) 5

d) 6

33. In a harmonic sequence, the 2nd term is 1/5, and the 4th term is 1/9. What is the 1st term?

a) 1/3

b) 1/4

c) 1/6

d) 1/7

34. The 5th term of an arithmetic sequence is 14, and the 9th term is 26. What is the 12th term?

a) 32

b) 34

p)c) 36

d) 38

35. The sum of the first 5 terms of a geometric series is 31, and the common ratio is 2. What is the first term?

a) 1

pb) 2

c) 3

d) 4

36. In an arithmetic sequence, the 4th term is 11, and the 8th term is 23. What is the sum of the first 10 terms?

a) 140

b) 150

c) 160

d) 170

37. The first term of a geometric sequence is 2, and the common ratio is 3. What is the sum of the first 8 terms?

a) 6560

b) 6561

c) 2186

d) 2187

38. The sum of an infinite geometric series is 24, and the first term is 16. What is the common ratio?

a) 1/3

b) 1/2

c) 2/3

d) 3/4

39. In an arithmetic sequence, the 3rd term is 8, and the 7th term is 20. What is the 15th term?

a) 44

b) 48

c) 52

d) 56

40. The first three terms of a geometric sequence are 5, 15, 45 the sum of the first 6 terms?

a) 364

b) 365

c) 728

d) 730

41. The sum of the first 7 terms of an arithmetic sequence is 91, and the first term is 1. What is the common difference?

a) 3

b) 4

c) 5

d) 6

42. In a harmonic sequence, the 3rd term is 1/7, and the 5th term is 1/11. What is the 2nd term?

a) 1/5

b) 1/6

c) 1/8

d) 1/9

43. The 6th term of an arithmetic sequence is 20, and the 10th term is 32. What is the 1st term?

a) 2

b) 4

c) 6

d) 8

44. The first term of a geometric series is 3, and the common ratio is 1/3. What is the sum of the infinite series?

a) 4.5

b) 4

c) 3.5

d) 3

45. In an arithmetic sequence, the 2nd term is 5, and the 5th term is 14. What is the 9th term?

a) 23

b) 25

c) 27

d) 29

46. The sum of the first 6 terms of a geometric series is 63, and the common ratio is 2. What is the first term?

a) 1

b) 2

c) 3

d) 4

47. The 4th term of an arithmetic sequence is 10, and the 8th term is 22. What is the sum of the first 6 terms?

a) 48

b) 54

p)c) 60

d) 66

48. In a geometric sequence, the 2nd term is 10, and the 4th term is 40. What is the common ratio?

a) 2

b) 3

c) 4

d) 5

49. The first term of an arithmetic sequence is 6, and the common difference is 5. What is the sum of the first 15 terms?

a) 570

b) 585

c) 600

d) 615

50. The sum of an infinite geometric series is 30, and the first term is 20. What is the common ratio?

a) 1/3

b) 1/2

c) 2/3

d) 3/4

Answers

1. a) 32

2. b) 162

3. c) 1

4. c) 13

5. a) 1/3

6. b) 7

7. b) 972

8. a) 5

9. d) 1/3

10. b) d) 4

11. a) 1

12. b) 216

13. a) 2

14. a) 210

15. d) 1/4

16. c) 45

17. b) 63

18. b) 6

19. c) 1/14

20. b) 59

21. b) 4

22. a) 4

23. b) 10

24. a) 31

25. a) 1

26. a) 1/3

27. b) 5

28. a) 570

29. c) 1/3

30. c) 1

31. a) 192

32. b) 4

33. a) 1/3

34. b) 35

35. a) 1

36. c) 155

37. b) 6560

38. c) 1/3

39. b) 44

40. b) 365

41. b) 4

42. b) 1/5

43. d) 4

44. a) 4.5

45. b) 26

46. a) 1

47. b) 48

48. a) 2

49. b) 585

50. c) 1/3

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