Find the AP, whose fourth term is 9 and sum of 6 and 13 term is 40
Answers
Answer:
3 , 5 , 7 , ................
Step-by-step explanation:
Given------> Fourth term of AP is 9 and sum of 6th and 13th term is 40 .
To find ------> Find the AP.
Solution-------> We know that, formula of nth term of AP be ,
aₙ = a + ( n - 1 ) d
Let , first term of AP be a and common difference be d.
ATQ, Fourth term of AP = 9
=> a₄ = 9
=> a + ( 4 - 1 ) d = 9
=> a + 3 d = 9
=> a = 9 - 3d
Now , ATQ,
a₆ + a₁₃ = 40
=> a + ( 6 - 1 ) d + a + ( 13 - 1 ) d = 40
=> a + 5 d + a + 12 d = 40
=> 2a + 17d = 40
Putting a = 9 - 3d , in it , we get,
=> 2 ( 9 - 3d ) + 17d = 40
=> 18 - 6d + 17d = 40
=> 11d = 40 - 18
=> 11d = 22
=> d = 22 / 11
=> d = 2
Now , a = 9 - 3d
Putting d = 2 in it we get,
=> a = 9 - 3 ( 2 )
=> a = 9 - 6
=> a = 3
First term = a = 3
Second term = a + d
= 3 + 2
= 5
Third term = a₂ + d
= 5 + 2
= 7
So AP is 3 , 5 , 7 , ................................