The n^{th} term of an A.P. is given by T_{n} | vedclass

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

Question

(A) Given the $n^{th}$ term of the $A.P.$ is $T_{n} = 4n + 7$.To find the first term $a$,substitute $n = 1$:$a = T_{1} = 4(1) + 7 = 11$.To find the se

Vedclass · Accepted Answer

$2n^{2} + 9n$

Vedclass · Answer

(A) Given the $n^{th}$ term of the $A.P.$ is $T_{n} = 4n + 7$.To find the first term $a$,substitute $n = 1$:$a = T_{1} = 4(1) + 7 = 11$.To find the second term,substitute $n = 2$:$T_{2} = 4(2) + 7 = 15$.The common difference $d$ is given by $d = T_{2} - T_{1} = 15 - 11 = 4$.The sum of $n$ terms of an $A.P.$ is given by the formula $S_{n} = \frac{n}{2}[2a + (n - 1)d]$.Substituting the values $a = 11$ and $d = 4$:$S_{n} = \frac{n}{2}[2(11) + (n - 1)4]$$S_{n} = \frac{n}{2}[22 + 4n - 4]$$S_{n} = \frac{n}{2}[4n + 18]$$S_{n} = n[2n + 9]$$S_{n} = 2n^{2} + 9n$.Thus,the sum of $n$ terms is $2n^{2} + 9n$.

The $n^{th}$ term of an $A.P.$ is given by $T_{n} = 4n + 7$. Find the sum of $n$ terms of this $A.P.$

Similar Questions

For the $A.P.$ $-2, -4, -6, -8, \ldots,$ the common difference is............

For an $A.P.$,the $12^{th}$ term is $4$ and the $20^{th}$ term is $-20$. Find the $n^{th}$ term of the $A.P.$

For the $A.P.$ $4, 8, 12, 16, \ldots$,$T_{40} - T_{30} = \ldots$

Determine whether the following sequence is an $A.P.$ or not. (Assume that the pattern continues.) If it is an $A.P.$,find its $n^{th}$ term: $1.4, 2.3, 3.2, 4.1, \dots$

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module