For an A.P.,the 3^{rd} term is 7 and the 7^{t | vedclass

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

Question

(B) Let the first term of the $A.P.$ be $a$ and the common difference be $d$.$T_n = a + (n - 1)d$Given $T_3 = 7$,so $a + 2d = 7$  --- $(1)$Given $T_7

Vedclass · Accepted Answer

$740$

Vedclass · Answer

(B) Let the first term of the $A.P.$ be $a$ and the common difference be $d$.$T_n = a + (n - 1)d$Given $T_3 = 7$,so $a + 2d = 7$  --- $(1)$Given $T_7 = 3(T_3) + 2$,so $a + 6d = 3(7) + 2 = 23$  --- $(2)$Subtracting equation $(1)$ from $(2)$:$(a + 6d) - (a + 2d) = 23 - 7$$4d = 16$$d = 4$Substituting $d = 4$ in equation $(1)$:$a + 2(4) = 7$$a + 8 = 7$$a = -1$The sum of the first $n$ terms is given by $S_n = \frac{n}{2}[2a + (n - 1)d]$.For $n = 20$:$S_{20} = \frac{20}{2}[2(-1) + (20 - 1)4]$$S_{20} = 10[-2 + 19(4)]$$S_{20} = 10[-2 + 76]$$S_{20} = 10[74] = 740$.Thus,the sum of the first $20$ terms is $740$.

For an $A.P.$,the $3^{rd}$ term is $7$ and the $7^{th}$ term exceeds thrice the $3^{rd}$ term by $2$. Find the sum of first $20$ terms of the $A.P.$

Similar Questions

The ratio of the sums of first $n$ terms of two $A.P.s$ is $(5n - 3) : (7n + 2)$. Find the ratio of their $m^{th}$ terms.

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

The $11^{\text{th}}$ term of the $AP: -5, \frac{-5}{2}, 0, \frac{5}{2}, \dots$ is

The list of numbers $-10, -6, -2, 2, \ldots$ is

The first term of a finite $A.P.$ is $5$ and its last term is $95$. If the common difference of the $A.P.$ is $5$,then there are $\ldots \ldots \ldots$ terms in the $A.P.$

Vedclass Test Series

Exam Paper Generator

Online Exam Module