Question

The sum of a geometric series of twelve terms with common ratio 2 is 20,475. What is the first term?

Answer 1

Answer: the first term is 5

Step-by-step explanation:

In a geometric sequence, the consecutive terms differ by a common ratio. The formula for determining the sum of n terms, Sn of a geometric sequence is expressed as

Sn = (ar^n - 1)/(r - 1)

Where

n represents the number of term in the sequence.

a represents the first term in the sequence.

r represents the common ratio.

From the information given,

S12 = 20475

r = 2

n = 12

Therefore,

20475 = (a × 2^(12) - 1)/2 - 1

20475 = (a × 4095)

20475 = 4095a

a = 20475/4095

a = 5