Use the geometric sum formula to nd out the value for this 1

Use the geometric sum formula to nd out the value for this: 1 + 3 + 3^2+ 3^3+ 3^4+... 3^15

2. Use the geometric sum formula to find out the value for this: 1 + 3 + 32 + 33 + 34 + … + 315

The given series is 1 + 3 + 3^2+ 3^3+ 3^4+... 3^15

Geometric series formula to find the sum of n terms is S_n= [a₁.(1-rⁿ)] / (1-r) where r is not equal to 1

here S_n is the sum of n terms in geometric progression

a₁ is the firstterm

r is the common ratio

n is the number of terms.

a₁= 1, a₂= 3, a₃= 9

r = a₂ / a₁

r = 3/1 = 3

In the given series there are total 16 terms, so n=16

By substituting the values in the formula we get, 1 + 3 + 3^2+ 3^3+ 3^4+... 3^15 as

S₁₆ = [1*(1-3^16)] / (1-3)

S₁₆= 1*21523360

Thus 1 + 3 + 3^2+ 3^3+ 3^4+... 3^15 is 21523360