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