- Trending Categories
- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP

- 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 Questions & Answers
- Find the Number of quadruples where the first three terms are in AP and last three terms are in GP using C++
- Find the first, second and third minimum elements in an array in C++
- Find the first, second and third minimum elements in an array in C++ program
- Sum of even Fibonacci terms in JavaScript
- Find if a number is part of AP whose first element and difference are given using C++.
- Find duplicate element in a progression of first n terms JavaScript
- Find sum of the series ?3 + ?12 +.... upto N terms in C++
- Mathematical Logical Terms and Definitions
- Sum of the first N terms of the series 2,10, 30, 68,…. in C programming
- Sum of the first N terms of the series 5,12, 23, 38…. in C Programming
- Find Pth term of a GP if Mth and Nth terms are given in C++
- Sum of the first N terms of the series 2, 6, 12, 20, 30…. in c programming
- Find sum of the series 1+22+333+4444+... upto n terms in C++
- Define the terms acquisition, takeover, merger and amalgamation
- Initialization, declaration and assignment terms in Java
- Common Terms Used in Lighting and Illumination

Advertisements