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5 votes
What is the sum of the series?

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

User Zeroin
by
8.9k points

2 Answers

4 votes

Answer:

255

Explanation:

User Pie Faced
by
8.2k points
4 votes

Answer:

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

User Hbf
by
8.2k points

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