Question

What is the sum of the series? 3+12+48+192+...+49,152

Answer 1

Answer:

65,535

Step-by-step explanation:

This is a geometric progression with r = 4

Since 12/3 = 4

48/12 = 4

etc.

Sum of geometric series = $S_n=\frac{a(r^n -1)}{r-1}$

Where

r is common ratio and a is first term, n is the number of terms

If we mutiply 192 by 4, we get 768,

768 * 4 = 3072

3072 * 4 = 12,288

12,288 * 4 = 49,152

Thus, if we count, we see there are 8 terms, so n = 8

Now putting everything in the formula, we get:

$S_n=\frac{a(r^n -1)}{r-1}\\S_{8}=\frac{3(4^8 -1)}{4-1}\\S_{8}=65,535$

The sum is 65,535