Question

What is the 32nd term of the arithmetic sequence where `a_1=13` and `a_13=-59`?

Answer 1

`32^(nd)` term is `-173`.

Explanation:

`n^(th)` term of an arithmetic sequence whose first term is `a_1` and common difference is `d` is `a_1+(n-1)d`.

Hence `a_13=a_1+(13-1)xxd=13` i.e. `13+12d=-59`

or `12d=-59-13=-72`

Hence `d=-72/12=-6` and `32^(nd)` term is

`a_(32)=a_1+(32-1)d=13+31xx(-6)`

= `13+(-186)=-173`