Home › JEE Main › mathematics › Sequences and Series › The sum to $n$ terms of a GP with first term $a …
The sum to $n$ terms of a GP with first term $a = 2$ and ratio $r = 3$ is:
A$2(3^n + 1)/2$, missing the $-1$ in the formula here
B$2\cdot 3^n$, ignoring the sum formula entirely
C$S_n = 2(3^n - 1)/(3 - 1) = 3^n - 1$, by the GP formula
D$2n\cdot 3^{n-1}$, the term-by-term sum on the worksheet
Answer & Solution
Correct answer: C. $S_n = 2(3^n - 1)/(3 - 1) = 3^n - 1$, by the GP formula
$S_n = a(r^n - 1)/(r - 1) = 2(3^n - 1)/2 = 3^n - 1$.
Related questions
Sum of GP: 1 + 1/2 + 1/4 + ... to infinity =GP with first term 2, common ratio 3. Find 5th term.Sum of first 20 natural numbers:The 10th term of the AP 3, 7, 11, ... is:The AM-GM INEQUALITY for two POSITIVE numbers $a$ and $b$ states thatIf the AM and GM of two positive numbers are $5$ and $4$ respectively, the numbers areThree numbers are in AP. Their sum is $24$ and their product is $440$. Find the smallest oSum of the CUBES of the first $n$ natural numbers, $1^3 + 2^3 + \ldots + n^3$, equals