An AP consists of 50 terms of which the 3^{rd | vedclass

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

Question

(B) Given that the $3^{rd}$ term $a_3 = 12$ and the total number of terms $n = 50$,with the last term $a_{50} = 106$.Using the formula for the $n^{th}

Vedclass · Accepted Answer

$64$

Vedclass · Answer

(B) Given that the $3^{rd}$ term $a_3 = 12$ and the total number of terms $n = 50$,with the last term $a_{50} = 106$.Using the formula for the $n^{th}$ term of an $AP$,$a_n = a + (n - 1)d$:For the $3^{rd}$ term: $a + 2d = 12$ $(i)$For the $50^{th}$ term: $a + 49d = 106$ $(ii)$Subtracting equation $(i)$ from $(ii)$:$(a + 49d) - (a + 2d) = 106 - 12$$47d = 94$$d = 2$Substituting $d = 2$ in equation $(i)$:$a + 2(2) = 12$$a + 4 = 12$$a = 8$Now,find the $29^{th}$ term $a_{29}$:$a_{29} = a + (29 - 1)d$$a_{29} = 8 + 28(2)$$a_{29} = 8 + 56 = 64$Thus,the $29^{th}$ term is $64$.

An $AP$ consists of $50$ terms of which the $3^{rd}$ term is $12$ and the last term is $106$. Find the $29^{th}$ term.

Similar Questions

$A$ 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 $m^3$).

Which term of the $AP : 3, 8, 13, 18, \ldots$ is $78$ (in $^{th}$)?

Which term of the $AP: 3, 15, 27, 39, \ldots$ will be $132$ more than its $54^{th}$ term?

How many terms of the $AP: 24, 21, 18, \ldots$ must be taken so that their sum is $78$?

In an $AP$,given $a=2, d=8, S_{n}=90$,find $n$ and $a_{n}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module