What will be the sum of the sequence up to 5th term 9, 36, 144, 576, ...? 3069 3070 3071 3072
Question
What will be the sum of the sequence up to 5th term 9, 36, 144, 576, ...?
3069
3070
3071
3072
Solution
This is a geometric sequence where each term is 4 times the previous term.
The sum of the first n terms of a geometric sequence can be found using the formula:
S_n = a * (r^n - 1) / (r - 1)
where:
- S_n is the sum of the first n terms,
- a is the first term,
- r is the common ratio, and
- n is the number of terms.
In this case, a = 9, r = 4, and n = 5.
So, the sum of the first 5 terms is:
S_5 = 9 * (4^5 - 1) / (4 - 1) S_5 = 9 * (1024 - 1) / 3 S_5 = 9 * 1023 / 3 S_5 = 3 * 1023 S_5 = 3069
So, the sum of the sequence up to the 5th term is 3069.
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