Find the sum of the first 25 terms of the A.P | vedclass

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

Question

(D) The given $A.P.$ is $30, 26, 22, \ldots$Here,the first term $a = 30$ and the common difference $d = 26 - 30 = -4$.The number of terms $n = 25$.The

Vedclass · Accepted Answer

$-450$

Vedclass · Answer

(D) The given $A.P.$ is $30, 26, 22, \ldots$Here,the first term $a = 30$ and the common difference $d = 26 - 30 = -4$.The number of terms $n = 25$.The formula for the sum of the first $n$ terms of an $A.P.$ is $S_n = \frac{n}{2} [2a + (n - 1)d]$.Substituting the values: $S_{25} = \frac{25}{2} [2(30) + (25 - 1)(-4)]$.$S_{25} = \frac{25}{2} [60 + (24)(-4)]$.$S_{25} = \frac{25}{2} [60 - 96]$.$S_{25} = \frac{25}{2} [-36]$.$S_{25} = 25 	imes (-18) = -450$.Thus,the sum of the first $25$ terms is $-450$.

Find the sum of the first $25$ terms of the $A.P.$ $30, 26, 22, \ldots$

Similar Questions

The sum of the first $n$ terms of an $A.P.$ is given by $S_{n} = \frac{3n^{2}}{2} + \frac{5n}{2}$. Find the $25^{th}$ term of the $A.P.$

Find the sum of the series: $7 + 10 \frac{1}{2} + 14 + \ldots + 84$.

In an $AP$,if $a = 1$,$a_{n} = 20$,and $S_{n} = 399$,then $n$ is:

Four numbers in increasing order form an $A.P.$ The sum of those numbers is $32$ and the ratio of the product of extremes to the product of means is $7: 15$. Find those numbers.

If the $n^{th}$ term of the $A.P.$ $9, 7, 5, \ldots$ and the $n^{th}$ term of the $A.P.$ $15, 12, 9, \ldots$ are equal,find the value of $n$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module