Find the sum of the geometric sequence (3, 6, 12, 24, ldots) up to the nth term.

Question

Accepted Answer

Step:1 ：First, we identify the common ratio of the sequence. Looking at the given sequence, we can see that each term is twice the previous term, so the common ratio (r) is 2.Step:2 ：The formula for the sum of the first n terms, (S_n), of a geometric sequence is (S_n = frac{a(1 - r^n)}{1 - r}), where (a) is the first term, (r) is the common ratio, and (n) is the number of terms.Step:3 ：Substituting the given values into the formula, we get (S_n = frac{3(1 - 2^n)}{1 - 2} = 3(2^n - 1)).

Answer

Step: 1 ：First, we identify the common ratio of the sequence. Looking at the given sequence, we can see that each term is twice the previous term, so the common ratio (r) is 2.Step: 2 ：The formula for the sum of the first n terms, (S_n), of a geometric sequence is (S_n = frac{a(1 - r^n)}{1 - r}), where (a) is the first term, (r) is the common ratio, and (n) is the number of terms.Step: 3 ：Substituting the given values into the formula, we get (S_n = frac{3(1 - 2^n)}{1 - 2} = 3(2^n - 1)).

Find the sum of the geometric sequence \(3, 6, 12, 24, \ldots\) up to the nth term.

Answer

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