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
[tex]a_1[/tex] be the first term and d be difference
Then the arithmetic progression will be ,
[tex]a_1 , (a_1+d),(a_1 +2d),......(a_1+(n-1)d)[/tex]
From the question ,
third term = 13
[tex](a_1 +2d) = 23[/tex]-------------(1)
Similarly
[tex](a_1 +4d) = 15[/tex]-----------------(2)
Subtracting (1) from (2) we get
-2d =8
[tex]d = \frac{8}{2}[/tex]
d = -4
Substituting d = 4 in equation 1, we get
[tex](a_1 +2(-4)) = 23[/tex]
[tex](a_1 -8) = 23[/tex]
[tex]a_1 = 23 +8[/tex]
[tex]a_1 = 31[/tex]
[tex]a_1 , (a_1+d),(a_1 +2d),......(a_1+(n-1)d)[/tex]
= 31 ,(31 +(-4)) ,(31 +2(-4)), (31+3(-4)).........
=> 31, 27, 23 , 19, 15, 11,7,3
