Question

find the sum of 8terms of a GP whose nth term is 3n

Answer 1

Answer:

Step-by-step explanation:

A8=A+7D put n(1),(2).

Then

A=3,D=3

A8=3+7(3)=24.

Answer 2

Answer:

The sum to 8 terms of a GP = 9840

Step-by-step explanation:

Given,

nth term of a GP = $3^n$

To find,

The sum of 8 terms of the GP

Solution

Recall the formula

The sum to n terms of a GP =  $\frac{a(r^n - 1)}{r-1}$, where a is the first term and r is the common ratio

Solution:

Given, the nth term of an GP =$a_n =$ $3^n$

First term = $a_1$ = 3

Second term = $a_2$ = 3² = 9

Third term = $a_3$ = 3³ = 27

Common ratio = $\frac{a_2}{a_1}$ = $\frac{9}{3}$ = 3

Sum to 8 terms of a GP = $S_8$ = $\frac{a(r^8 - 1)}{r-1}$

Substituting the value of a and r we get

$S_8$ = $\frac{3(3^8 - 1)}{3-1}$

=  $\frac{3(3^8 - 1)}{2}$

=$\frac{3(6561 - 1)}{2}$

=$\frac{3X 6560}{2}$

=3×3280

$S_8$ = 9840

∴The sum to 8 terms of a GP = 9840

#SPJ3