For an A.P.,the first term is 10,the n^{th} t | vedclass

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

Question

(A) Given: First term $a = 10$,$n^{th}$ term $a_n = 40$,and sum of $n$ terms $S_n = 150$.We know the formula for the sum of an $A.P.$ is $S_n = \frac{

Vedclass · Accepted Answer

$n=6, d=6$

Vedclass · Answer

(A) Given: First term $a = 10$,$n^{th}$ term $a_n = 40$,and sum of $n$ terms $S_n = 150$.We know the formula for the sum of an $A.P.$ is $S_n = \frac{n}{2}(a + a_n)$.Substituting the given values: $150 = \frac{n}{2}(10 + 40)$.$150 = \frac{n}{2}(50)$.$150 = 25n$.$n = \frac{150}{25} = 6$.Now,we use the formula for the $n^{th}$ term: $a_n = a + (n - 1)d$.Substituting the values: $40 = 10 + (6 - 1)d$.$40 - 10 = 5d$.$30 = 5d$.$d = \frac{30}{5} = 6$.Thus,$n = 6$ and $d = 6$.

For an $A.P.$,the first term is $10$,the $n^{th}$ term is $40$,and the sum of the first $n$ terms is $150$. Find the value of $n$ and the common difference $d$.

Similar Questions

For an $A.P.$,the first term is $10$ and the $10^{th}$ term is $100$. Then,the sum of the first $10$ terms is..........

There are $\ldots \ldots \ldots \ldots$ multiples of $3$ lying between $1$ and $50$.

If $7$ times the $7^{\text{th}}$ term of an $AP$ is equal to $11$ times its $11^{\text{th}}$ term,then its $18^{\text{th}}$ term will be

The number of terms in the finite $A.P.$ $13, 26, 39, \ldots, 650$ is ........

Which term of the $A.P.$ $85, 78, 71, \ldots$ is its first negative term? If the order of this term is $n$,find $S_{n}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module