- Trending Categories
- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- MS Excel
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP
- Physics
- Chemistry
- Biology
- Mathematics
- English
- Economics
- Psychology
- Social Studies
- Fashion Studies
- Legal Studies

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who

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

Given:

The second term of an A.P. is 14 and the third term is 18.

To do:

We have to find the sum of the first 51 terms of the A.P.

Solution:

Let the first term and the common difference of the A.P. be $a$ and $d$ respectively.

We know that,

$a_n=a+(n-1)d$

This implies,

$a_2=a+(2-1)d$

$14=a+d$

$a=14-d$.......(i)

$a_3=a+(3-1)d$

$18=a+2d$

$18=14-d+2d$ (From (i))

$d=18-14$

$d=4$

Therefore,

$a=14-d$

$=14-4$

$=10$

We know that,

$S_{n}=\frac{n}{2}[2 n+(n-1) d]$

$S_{51}=\frac{51}{2}[2 \times(10)+(51-1) \times 4]$

$=\frac{51}{2}[20+50 \times 4]$

$=\frac{51}{2}(20+200)$

$=\frac{51}{2} \times 220$

$=51 \times 110$

$=5610$

The sum of the first 51 terms of the A.P. is $5610$.

- Related Articles
- Find the sum of first 51 terms of an A.P. whose second and third terms are 14 and 18 respectively.
- Find the sum of first 17 terms of an AP whose \( 4^{\text {th }} \) and \( 9^{\text {th }} \) terms are \( -15 \) and \( -30 \) respectively.
- How many terms are there in the A.P. whose first and fifth terms are $-14$ and $2$ respectively and the sum of the terms is $40$?
- The sum of the first five terms of an AP and the sum of the first seven terms of the same AP is 167. If the sum of the first ten terms of this AP is 235 , find the sum of its first twenty terms.
- The sum of first 7 terms of an AP is 49 and that of 17 terms is 289. Find the sum of first n terms .
- The sum of three terms of an A.P. is 21 and the product of the first and the third terms exceeds the second term by 6, find three terms.
- If sum of first 6 terms of an AP is 36 and that of the first 16 terms is 256 , find the sum of first 10 terms.
- The first and the last terms of an AP are 7 and 49 respectively. If sum of all its terms is 420, find its common difference.
- If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first $n$ terms.
- If the first, second and third terms of a proportion are respectively 45, 6 and 15, find the fourth term.
- If the sum of first four terms of an A.P. is 40 and that of first 14 terms is 280. Find the sum of its first n terms.
- The first and the last terms of an AP are 5 and 45 respectively. If the sum of all its terms is 400, Find its common difference.
- The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.
- The sum of first 6 terms of an \( \mathrm{AP} \) is 36 and the sum of its first 16 terms is 256. Find the sum of first 10 terms of this \( A P \).
- The sum of the third term and the seventh term of an AP is 6 and their product is 8. Find the sum of first sixteen terms of the AP?

Advertisements