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

October 1, 2021 | education

| **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.

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