Question

How many terms of G.P. 3, 3^2, 3^3, ... are needed to give the sum 120 ?​

Answer 1

Answer:

4 terms are required

Step-by-step explanation:

In the given GP , first term = 3, common ratio is 3

sum is 120

formula for sum in GP is --

$(a( {r}^{n} - 1)) \div (r - 1)$

Here a = first term, r = commin ratio

putting the values ,

$(3 \times ( {3}^{n} - 1)) \div (3 - 1)$

3((3^n)-1 )/2 = 120

3^n -1 = 80

3^n = 81

therefore , n = 4 is answer

since 3^4 = 81