Let a_1, a_2, ldots, a_{2024} be an Arithmeti | vedclass

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

Question

(D) Let the given sum be $S = a_1 + (a_5 + a_{10} + \ldots + a_{2020}) + a_{2024} = 2233$. In an $A.P.$,the sum of terms equidistant from the beginnin

Vedclass · Accepted Answer

$11132$

Vedclass · Answer

(D) Let the given sum be $S = a_1 + (a_5 + a_{10} + \ldots + a_{2020}) + a_{2024} = 2233$. In an $A.P.$,the sum of terms equidistant from the beginning and end is constant,i.e.,$a_k + a_{n-k+1} = a_1 + a_n$. Here,$n = 2024$. The terms in the bracket are $a_{5k}$ for $k=1$ to $404$. Note that $a_5 + a_{2020} = a_1 + a_{2024}$,$a_{10} + a_{2015} = a_1 + a_{2024}$,and so on. There are $404$ terms in the sequence $5, 10, \ldots, 2020$. Pairing these terms,we have $202$ pairs,each equal to $(a_1 + a_{2024})$. Including the outer terms $a_1$ and $a_{2024}$,the total sum is $203(a_1 + a_{2024}) = 2233$. Thus,$(a_1 + a_{2024}) = \frac{2233}{203} = 11$. The sum of the $A.P.$ is $S_{2024} = \frac{2024}{2}(a_1 + a_{2024}) = 1012 	imes 11 = 11132$.

Let $a_1, a_2, \ldots, a_{2024}$ be an Arithmetic Progression such that $a_1 + (a_5 + a_{10} + a_{15} + \ldots + a_{2020}) + a_{2024} = 2233$. Then $a_1 + a_2 + a_3 + \ldots + a_{2024}$ is equal to . . . . . .

Similar Questions

If the sides of a right-angled triangle are in $A.P.$,then the sides are proportional to

If the sides of a right-angled triangle are in $A.P.$,then their ratio is:

Let $S_n$ and $s_n$ denote the sum of the first $n$ terms of two different arithmetic progressions $(A.P.)$ for which $\frac{s_n}{S_n} = \frac{3n - 13}{7n + 13}$. Find the ratio $\frac{s_n}{S_{2n}}$.

Let $a_1, a_2, a_3, \ldots$ be in an arithmetic progression of positive terms. Let $A_{k}=a_1^2-a_2^2+a_3^2-a_4^2+\ldots+a_{2k-1}^2-a_{2k}^2$. If $A_3=-153$,$A_5=-435$ and $a_1^2+a_2^2+a_3^2=66$,then $a_{17}-A_7$ is equal to:

If $< a_n >$ is an $A.P.$ and $a_1 + a_4 + a_7 + \dots + a_{16} = 147$,then $a_1 + a_6 + a_{11} + a_{16}$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module