1st term of geometric sequence is 1/2 and 9th term is 128. Find sum of 5th term?

31/2 or 15½

Step-by-step explanation:

From the question given above, the following data were obtained:

First term (a) = ½

9th term (T₉) = 128

Sum of 5th term (S₅) =?

Next, we shall determine determine the common ratio of the sequence. This can be obtained as follow:

First term (a) = ½

9th term (T₉) = 128

Common ratio (r) =?

T₉ = ar⁸

128 = ½ × r⁸

Cross multiply

r⁸ = 128 × 2

r⁸ = 256

Express 256 in index form with 2 as the base

r⁸ = 2⁸

r = 2

Finally, we shall determine the sum of the 5th term. This can be obtained as follow:

First term (a) = ½

Common ratio (r) =

Number of term (n) = 5

Sum of 5th term (S₅) =?

Sₙ = a[rⁿ – 1] / r – 1

S₅ = ½[2⁵ – 1] / 2 – 1

S₅ = ½[32 – 1] / 1

S₅ = ½ × 31

S₅ = 31/2 or 15½

Thus, the sum of the 5th term of the sequence is 31/2 or 15½

1. 3.4/4

2. 0.8/7

3. 0.5 x 3

4. 0.9 x 6

5. 10.8

6. 2.35

7. 0.567

8. 9.35

9. 0.02

10. 0.06

11. 0.16

12. 0.42

13. 0.63

14. 5.6

15. 8.1

16. 9.9

17. 0.28

18. 0.48

19. 0.27

20. 0.49

21. 0.45

22. 0.72

23. 0.9

24. 0.88

25. 0.75

26. 0.16

27. 0.328

28. 0.495

29. 0.72

30. 1.068