Question

What is the 17th term in the arithmetic sequence in which `a_6` is 101 and `a_9` is 83?

Answer 1

`17^(th)` term is `35`

Explanation:

`n^(th)` term of an arithmetic sequence `{a,a+d,a+2d,........}`, whose first term is `a` and difference between a term and its preceeding term is `d`, is `a+(n-1)d`.

As `6^(th)` term is `101`, we have `a+5d=101` and .......(1)

as `9^(th)` term is `83`, we have `a+8d=83`. ......(2)

Subtracting (1) from (2), we get `3d=-18` i.e, `d=-6`

Putting this in (1), we get `a-30=101` or `a=131`

Hence, `17^(th)` term is `131+16xx(-6)=131-96=35`