Question

if the first term of G.P is 729 and 7th term is 64, find the sum of 7 terms​

Answer 1

Step-by-step explanation:

The nth term of a Geometric Progression is given by the formula

T(n)=a∗r(n−1)

Sum of n terms of a Geometeric Progression is given by the formula

S(n)=a(1−r(n−1))/(1−r)

Here 'a' is the first term and 'r' is the common difference.

If you know the above formulas, then solving this question should be pretty simple. We are given

a = 729

T(7) = 64

=> ar^(7-1) = 64

=> 729*r^6 = 64

=> r^6 = 64/729 = (2/3)^6

=> r = 2/3

Now, we need to find out the sum of the first 7 terms

S(7) = 729 * (1 - (2/3)^6) / (1-2/3)

=> S(7) = 729 * ( (729-64) / 729) / (1/3) )

=> S(7) = 729 * (665/243)

=> S(7) = 1995

So, the sum of the first 7 terms of the Geometric Progression (GP) is 1995