If the sum of the first 2n terms of 2, 5, 8, | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) For the first arithmetic progression $(2, 5, 8, \dots)$: First term $a_1 = 2$, common difference $d_1 = 3$. The sum of the first $2n$ terms is $S_

Vedclass · Accepted Answer

$11$

Vedclass · Answer

(C) For the first arithmetic progression $(2, 5, 8, \dots)$: First term $a_1 = 2$, common difference $d_1 = 3$. The sum of the first $2n$ terms is $S_{2n} = \frac{2n}{2} [2(2) + (2n - 1)3] = n [4 + 6n - 3] = n(6n + 1)$.For the second arithmetic progression $(57, 59, 61, \dots)$: First term $a_2 = 57$, common difference $d_2 = 2$. The sum of the first $n$ terms is $S_n = \frac{n}{2} [2(57) + (n - 1)2] = \frac{n}{2} [114 + 2n - 2] = \frac{n}{2} [112 + 2n] = n(56 + n)$.Given that $S_{2n} = S_n$, we have $n(6n + 1) = n(56 + n)$.Since $n 
eq 0$, we divide by $n$: $6n + 1 = 56 + n$.$5n = 55$, which gives $n = 11$.

If the sum of the first $2n$ terms of $2, 5, 8, \dots$ is equal to the sum of the first $n$ terms of $57, 59, 61, \dots$, then $n$ is equal to

Similar Questions

If $p$ times the $p^{th}$ term of an $A.P.$ is equal to $q$ times the $q^{th}$ term of an $A.P.$,then the $(p + q)^{th}$ term is

The ${20^{th}}$ term of the series $2 \times 4 + 4 \times 6 + 6 \times 8 + \dots$ will be

The first term of an $A.P.$ of consecutive integers is $p^2 + 1$. The sum of $(2p + 1)$ terms of this series can be expressed as:

If the ${p^{th}}$ term of an $A.P.$ is $q$ and the ${q^{th}}$ term is $p$,then its ${r^{th}}$ term will be

If $b$ is the first term of an infinite $G.P.$ whose sum is $5$,then $b$ lies in the interval

Vedclass Test Series

Exam Paper Generator

Online Exam Module