Find the sum of the six terms of the sequence 8, -2, 1/2, -1/8,

Correct Answer is : 819128819/128128819

Correct Answer is : 819128819/128128819

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Progression Practice Test 1

Question : 15 of 23

Marks: +1, -0

8, -2, \frac{1}{2}, -\frac{1}{8}, \ldots

Solution: 👈: Video Solution

Concept:

The given sequence is a geometric progression, so use the formula for the sum of

n

terms.

Explanation:

First term:

a=8

Common ratio:

r=\frac{-2}{8}=-\frac{1}{4}

Number of terms:

n=6

Use the sum formula:

S_n=\frac{a(1-r^n)}{1-r},\quad r\ne 1.

Substitute the values:

S_6=\frac{8\left(1-\left(-\frac{1}{4}\right)^6\right)}{1-\left(-\frac{1}{4}\right)}.

Since

\left(-\frac{1}{4}\right)^6=\frac{1}{4096}

and

1-\left(-\frac{1}{4}\right)=\frac{5}{4}

S_6=\frac{8\left(1-\frac{1}{4096}\right)}{\frac{5}{4}}.

Simplify:

S_6=8\cdot\frac{4095}{4096}\cdot\frac{4}{5}=\frac{819}{128}.

Answer:

\frac{819}{128}

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