Geometric progression problem

Question

b_n=3*2^n-1 is a geometric progression. Find the sum of its first three terms.

Answer 1

bn = 3(2)^(n-1) common ratio = 2 = 4

bn=a1(r^(n-1) a1 = first term

b1 = 3

b2 = 3(2) = 6

b3 = 3(40) =12

sum = b1+b2+b3 = 3+6+12= 21

Sn = a1(1-r^n)/(1-r) is the general formula for partial sum of a geometric series

for first 3 terms, n=3

S3 = 3(1-2^3)/(1-2)

= 3(1-8)/-1

=3(-7)/-1

= 21 = sum of first 3 terms