a problem on arithmetic progression

Topic:- Arithmetic progressions

Arithmetic progression (A.P.) is a sequence of numbers such that the difference of any two successive members of the sequence is a constant. For instance, the sequence 3, 5, 7, 9, 11, 13... is an arithmetic progression with common difference 2.
If the initial term of an arithmetic progression is a₁ and the common difference of successive members is d, then the nth term of the sequence is given by:

and in general

A finite portion of an arithmetic progression is called a finite arithmetic progression and sometimes just called an arithmetic progression.
Question:-
Given that 5 th term and 12 th term s of an arithmetic progression are 11 and 25 respectively .find "a" and "d".

Solution:-

Given 5 th term = 11

a+4d = 11 ----1

Given 12 th term = 25

a+11d=25 -----2


Subtract 1 from 2


a + 11d = 25

a + 4d = 11
(-)
-------------------

7d = 14

d = 2

Substitute d=2 in 1

a + 4d = 11

a + 4(2)= 11

a + 8 = 11

a = 11-8

a = 3


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