the first and last terms of a geometric progression are 2 and 2048 respectively. the sum of the series is 2730. find the number of terms and the common ratio

n=6

Step-by-step explanation:

Sn = (g1-gn. r) / (1-r)

2730 = (2-2948r) / (1-r)

2730 (1-r) = 2-2048r

2730-2730r=2 - 2048r

682r=2729

r=4, common ratio

Now using the formula; Gn=G1. r∧n-1

2048=2.4∧n-1

2048=4∧n-1=2∧2n-2

㏒2 1024=㏒2 2∧2n-2

10=2n-2

n=12/2

=6