A geometric progression with denominator q = 2, the sum of the first eight terms is 635.

A geometric progression with denominator q = 2, the sum of the first eight terms is 635. Find the sixth term of this progression

1. The sixth term of the geometric progression will be calculated by the formula

bn = b1 * g ^ (n – 1).

So, first you need to find out the value of b1 with a known g = 2.

2. For this we use the set value

S8 = 635.

Let’s write down the general formula for the S8

Sn = (bn * g – b1): (g – 1) and substitute in the given S8 = (b8 * 2 – b1): (2 – 1) = (b1 * 2 ^ 7 – b1): 1 = (b1 * 128 – b1) = 635, whence 128 b1 – b1 = 635,

then b1 = 635: 127 = 5.

3. Finally, calculate b6 = b1 * g ^ 5 = 5 * 2 ^ 7 = 5 * 32 = 160.

Answer: The sixth term is 160.