In an AP given a_{n}=4, d=2, S_{n}=-14,find n | vedclass

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

Question

(A) Given that,$a_{n}=4, d=2, S_{n}=-14$.Using the formula for the $n^{th}$ term of an $AP$:$a_{n} = a + (n - 1)d$$4 = a + (n - 1)2$$4 = a + 2n - 2$$a

Vedclass · Accepted Answer

$n=7, a=-8$

Vedclass · Answer

(A) Given that,$a_{n}=4, d=2, S_{n}=-14$.Using the formula for the $n^{th}$ term of an $AP$:$a_{n} = a + (n - 1)d$$4 = a + (n - 1)2$$4 = a + 2n - 2$$a = 6 - 2n$  --- $(i)$Using the formula for the sum of $n$ terms of an $AP$:$S_{n} = \frac{n}{2}[a + a_{n}]$$-14 = \frac{n}{2}[a + 4]$$-28 = n(a + 4)$Substitute $a = 6 - 2n$ from $(i)$ into the equation:$-28 = n(6 - 2n + 4)$$-28 = n(10 - 2n)$$-28 = 10n - 2n^{2}$$2n^{2} - 10n - 28 = 0$$n^{2} - 5n - 14 = 0$$(n - 7)(n + 2) = 0$Since $n$ must be a positive integer,$n = 7$.Substitute $n = 7$ into equation $(i)$:$a = 6 - 2(7)$$a = 6 - 14$$a = -8$Thus,$n = 7$ and $a = -8$.

In an $AP$ given $a_{n}=4, d=2, S_{n}=-14$,find $n$ and $a$.

Similar Questions

Find the sum of first $22$ terms of an $AP$ in which $d=7$ and $22^{nd}$ term is $149$.

Are $2, 4, 8, 16, \ldots$ in an $AP$? If they form an $AP$,find the common difference $d$ and write three more terms.

$A$ small terrace at a football ground comprises of $15$ steps each of which is $50 \, m$ long and built of solid concrete. Each step has a rise of $\frac{1}{4} \, m$ and a tread of $\frac{1}{2} \, m$. Calculate the total volume of concrete required to build the terrace (in $m^3$).

Find the sum of the first $24$ terms of the list of numbers whose $n^{th}$ term is given by $a_{n} = 3 + 2n$.

The $17^{th}$ term of an $AP$ exceeds its $10^{th}$ term by $7$. Find the common difference.

Vedclass Test Series

Exam Paper Generator

Online Exam Module