Question

The nth term of an AP is 12-4n. Find the first term and the common difference.

Answer 1

the first term is 8 and common difference d is -4.

Explanation:

We are given nth term of an arithmetic sequence is: aₙ=12-4n

We need to find first term and common difference of given arithmetic sequence

First term can be found by putting n=1:

`a_n=12-4n\\a_1=12-4(1)\\a_1=12-4\\a_1=8`

So, first term is a₁= 8

Now to find common difference we need to find second term

Second term can be found by putting n=2

`a_n=12-4n\\a_2=12-4(2)\\a_2=12-8\\a_2=4`

So, second term is: 4

The common difference is found by subtracting second term with first term: a₂-a₁= 4-8 = -4

So, first term is 8 and common difference d is -4