Question

Find the sum of the series.
a) 3 + 12 + 48 + ... + 768​

Answer 1

1023

Explanation:

r = 12/3 = 48/12 = 4

The constant ratio is 4.

Method 1:

Write out the series and add the terms.

3 + 12 + 48 + 192 + 768 = 1023

Method 2:

Use the formula.

S_n = [a_1(1 - r^n)]/(1 - r)

S_5 = [3(1 - 4^5)]/(1 - 4)

S_5 = [3(1 - 1024)]/(-3)

S_5 = -(-1023)

S_5 = 1023