Question

If The 3rd term of an A.S is and 5th term is . What is an A.P?​

Answer 1

Question:

If The 3rd term of an A.S 23 is and 5th term is 15 .P What is an A.?​

Answer:

A.P is 31, 27, 23 ,19, 15, 11, 7, 3

Explanation:

Given:

3rd term = 23

5th term = 15

To Find:

The arithmetic Progression = ?

Solution:

Let

`a_1` be the first term and d be difference

Then the arithmetic progression will be ,

`a_1 , (a_1+d),(a_1 +2d),......(a_1+(n-1)d)`

From the question ,

third term = 13

`(a_1 +2d) = 23`-------------(1)

Similarly

`(a_1 +4d) = 15`-----------------(2)

Subtracting (1) from (2) we get

-2d =8

`d = (8)/(2)`

d = -4

Substituting d = 4 in equation 1, we get

`(a_1 +2(-4)) = 23`

`(a_1 -8) = 23`

`a_1 = 23 +8`

`<strong>a_1 = 31</strong>`

`a_1 , (a_1+d),(a_1 +2d),......(a_1+(n-1)d)`

= 31 ,(31 +(-4)) ,(31 +2(-4)), (31+3(-4)).........

=> 31, 27, 23 , 19, 15, 11,7,3