Question

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

Answer 1

Hey User!

GIVEN:

The eighth term of G.P. is 640.

The third term of G.P. is 20.

TO FIND:

The sum of first seven terms.

FORMULA USED:

Tnth = a*r^(n-1)

Sn = a(r^n - 1)/(r-1)

where, a is the first term of the GP

r is the common ratio of the G.P.

n is the number of terms

Tnth = The nth term.

Sn = Sum of first n terms.

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.

Hope it helps............have a nice day :)