Question

The sum of the third and the seventh terms of an Ap is 6 and their product is 8.find the sum of first sixteen term of ap.z

Answer 1

Let the first term of AP be a and
The common difference between d
We know that nth term of AP is (a+(n-1)d)
Third term = a+2d
Seventh term =a+6d
Given sum of 3rd and 7th term of AP is 6
=>a+2d+a+6d=6
2a+8d=6
a+4d=3 -----------(1)
=>a=3-4d
Given product of 3rd and 7th terms is 8
=>(a+2d)(a+6d)=8
(a+2d)(a+4d+2d)=8
(a+2d)(3+2d)=8 [from (1)]
(3-4d+2d)(3+2d)=8
(3-2d)(3+2d)=8
3^2-(2d)^2=8
9-4d^2=8
4d^2=1
d^2=1/4
d=1/2 or -1/2
Substitute in a=3-4 d
d=1/2 or d=-1/2
a=3-4 (1/2) | a=3-4 (-1/2)
a=3-2 | a=3+2
a=1 | a=5

Sixteenth term=a+15d
If d=1/2 , a=1
T16=1+15/2=17/2

If d=-1/2 , a=5
T16=5+15(-1/2)=5-15/2=-5/2

Therefore 16th term of AP is -5/2 or 17/2



IF IT HELPS PLZ MARK AS BRAINLIEST ANSWER