If a_1, a_2, a_3, dots, a_n are in A.P. and a | vedclass

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

Question

(A) The given sum is $a_1 + a_4 + a_7 + a_{10} + a_{13} + a_{16} = 114$.This is an arithmetic progression with $6$ terms,where the first term is $a_1$

Vedclass · Accepted Answer

$76$

Vedclass · Answer

(A) The given sum is $a_1 + a_4 + a_7 + a_{10} + a_{13} + a_{16} = 114$.This is an arithmetic progression with $6$ terms,where the first term is $a_1$ and the last term is $a_{16}$.The sum of an $A.P.$ is given by $S_n = \frac{n}{2}(first + last)$.Thus,$\frac{6}{2}(a_1 + a_{16}) = 114$.$3(a_1 + a_{16}) = 114 \Rightarrow a_1 + a_{16} = 38$.We need to find the sum $S = a_1 + a_6 + a_{11} + a_{16}$.This is also an arithmetic progression with $4$ terms,where the first term is $a_1$ and the last term is $a_{16}$.$S = \frac{4}{2}(a_1 + a_{16}) = 2(38) = 76$.

If $a_1, a_2, a_3, \dots, a_n$ are in $A.P.$ and $a_1 + a_4 + a_7 + \dots + a_{16} = 114$,then $a_1 + a_6 + a_{11} + a_{16}$ is equal to

Similar Questions

If the sum of the first $10$ terms of an arithmetic progression is $4$ times the sum of its first $5$ terms,then the ratio of its first term to the common difference is......

Let $T_r$ be the $r$-th term of an arithmetic progression for $r = 1, 2, 3, \dots$. If for some positive integers $m$ and $n$,$T_m = \frac{1}{n}$ and $T_n = \frac{1}{m}$,then $T_{mn} = \dots$

If the middle term of the $AP$ is $300$,then the sum of its first $51$ terms is

If $\log _{10} 2, \log _{10} (2^x - 1), \log _{10} (2^x + 3)$ are in $A.P.,$ then :-

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module