If the sum of a certain number of terms of th | vedclass

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

Question

(A) Let the sum of $n$ terms of the given $A.P.$ be $116$.$S_{n} = \frac{n}{2}[2a + (n - 1)d]$Here,$a = 25$ and $d = 22 - 25 = -3$.$	herefore 116 = \

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(A) Let the sum of $n$ terms of the given $A.P.$ be $116$.$S_{n} = \frac{n}{2}[2a + (n - 1)d]$Here,$a = 25$ and $d = 22 - 25 = -3$.$	herefore 116 = \frac{n}{2}[2 	imes 25 + (n - 1)(-3)]$$\Rightarrow 232 = n(50 - 3n + 3)$$\Rightarrow 232 = 53n - 3n^{2}$$\Rightarrow 3n^{2} - 53n + 232 = 0$$\Rightarrow 3n^{2} - 24n - 29n + 232 = 0$$\Rightarrow 3n(n - 8) - 29(n - 8) = 0$$\Rightarrow (n - 8)(3n - 29) = 0$Since $n$ must be a positive integer,$n = 8$.$	herefore a_{8} = a + (8 - 1)d = 25 + 7(-3) = 25 - 21 = 4$.Thus,the last term of the $A.P.$ is $4$.

If the sum of a certain number of terms of the $A.P.$ $25, 22, 19, \ldots$ is $116$,find the last term.

Similar Questions

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

Three numbers are in $A.P.$ whose sum is $33$ and product is $792$. The smallest number among these is:

What is the sum of $n$ arithmetic means between $a$ and $b$?

Given that $n$ $A$.$M$.'s are inserted between two sets of numbers $a, 2b$ and $2a, b$,where $a, b \in R$. Suppose further that the $m^{th}$ mean between these sets of numbers is the same,then the ratio $a:b$ equals

Which term of the sequence $5, 8, 11, 14, \dots$ is $320$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module