Question

What is the sum of the series?

3+12+48+192+...+49,152

Answer 1

255

Explanation:

Answer 2

65,535

Explanation:

This is a geometric progression with r = 4

Since 12/3 = 4

48/12 = 4

etc.

Sum of geometric series =
`S_n=(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=(a(r^n -1))/(r-1)\\S_(8)=(3(4^8 -1))/(4-1)\\S_(8)=65,535`

The sum is 65,535