Find the sum of the first 51 terms of an AP w | vedclass

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

Question

(D) Given that,the second term $a_{2} = 14$ and the third term $a_{3} = 18$.The common difference $d$ is given by $d = a_{3} - a_{2} = 18 - 14 = 4$.Si

Vedclass · Accepted Answer

$5610$

Vedclass · Answer

(D) Given that,the second term $a_{2} = 14$ and the third term $a_{3} = 18$.The common difference $d$ is given by $d = a_{3} - a_{2} = 18 - 14 = 4$.Since $a_{2} = a + d$,we have $14 = a + 4$,which gives the first term $a = 10$.The sum of the first $n$ terms of an $AP$ is given by $S_{n} = \frac{n}{2}[2a + (n - 1)d]$.For $n = 51$,$S_{51} = \frac{51}{2}[2(10) + (51 - 1)4]$.$S_{51} = \frac{51}{2}[20 + (50)(4)]$.$S_{51} = \frac{51}{2}[20 + 200] = \frac{51}{2}(220)$.$S_{51} = 51 	imes 110 = 5610$.

Find the sum of the first $51$ terms of an $AP$ whose second and third terms are $14$ and $18$ respectively.

Similar Questions

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

$A$ sum of ₹ $1000$ is invested at $8 \%$ simple interest per year. Calculate the interest at the end of each year. Do these interests form an $AP$? If so,find the interest at the end of $30 \text{ years}$ making use of this fact. (in ₹)

Write the first four terms of the $AP,$ when the first term $a$ and the common difference $d$ are given as follows: $a = -1, d = \frac{1}{2}$

Are $\sqrt{3}, \sqrt{6}, \sqrt{9}, \sqrt{12}, \ldots$ in an $AP$? If they form an $AP$,find the common difference $d$ and write three more terms.

Find the sum of the first $15$ multiples of $8.$

Vedclass Test Series

Exam Paper Generator

Online Exam Module