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

Step-by-step 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

$d = \frac{8}{2}$

d = -4

Substituting d = 4 in equation 1, we get

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

$(a_1 -8) = 23$

$a_1 = 23 +8$

$a_1 = 31$

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

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

=>  31, 27, 23 , 19, 15, 11,7,3