The sun of the 5th and the 7th terms of an AP is 52 and the 10th term is 46. Find the AP.

Answer

The required A.P. is `1, 6, 11, 16, ….`

Explanation

Here, `t_(10)=46, t_(5)+t_(7)=52`
`t_(n)=a+(n-1)d` ...(Formula)
`thereforet_(10)=a+(n-1)d`
`therefore46=a+9d`
`thereforea+9d=46" "....(1)`
`t_(5)+t_(7)=[a+(5-1)d]+[a+(7-1)d]` …(From the formula)
`therefore52=a+4d+a+6d`
`therefore52=2a+10d`
`therefore26=a+5d` ...(Dividing both sides by 2) ,
`thereforea+5d=26" "...(2)`
Subtracting equation (2) from equation (1),
`a+9d=46" "...(1)`
`-a+5d=26 " "...(2)`
Subtracting the equation (2) from equation (1).
`a+9d=46" "...(1)`
`-a+5d=26" "...(2)`
`(---)/(4d=20)`
`therefored=5` Substituting `d=5` in equation (2),
`a+5(5)=26 " "thereforea+25=26`
`thereforea=26-26 " "thereforea=1`
The first term of the A.P. is 1 and common difference`=d=5`.
So,`a=t_(1)=1,t_(2)=t_(1)+d=1+5=6,t_(3)=t_(2)+d=6+5=11.`