Question

The eighth term of a geometric sequence is 640. The third term is 20. Find the sum
of the first 7 terms.

Answer 1

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SOLUTION:

ATQ, we have

T8 = 640

ar^7 = 640.....(1)

Also, T3 = 20

ar^2 = 20...(2)

eq(1)/eq(2), we get

r^5 = 32

r = 2.

So, the common ratio will be 2.

Now, putting r = 2 in eq(1), we get

a(128) = 640

a = 5.

So, the first term is 5 and the common ratio is 2.

Now, the sum of the first 7 terms will be..

S7 = 5(2^7 -1)/(2-1)

S7 = 5(128-1)

S7 = 5*(127)

S7 = 635.

So, the sum of the first 7 terms of the given G.P. will be 635.

ADDITIONAL INFORMATION:

If the G.P. is decreasing(ie, r is smaller than 1) , then the sum of infinite terms of the G.P. is given by.....S(infinity) = a/(1-r).

For an increasing G.P., the sum of infinite terms is also infinite.

Hope this helps