Question

Given the indicated terms of an arithmetic sequence a3=1, a33=22 find the first term

Answer 1

The first term is a = 0.4.

Explanation:

We are given the indicated terms of an arithmetic sequence;
`a_3` = 1,
`a_3_3` = 22.

As we know that the nth term of the A.P. is given by;

`a_n=a+(n-1)d`

where, a = first term and d = common difference

Now, the third term of AP is given as 1, this means;

`a_3=a+(3-1)d`

`a+2d=1`

a = 1 - 2d --------------- [equation 1}

Also, the 33rd term of AP is given as 22, this means;

`a_3_3=a+(33-1)d`

`a+32d=22`

`1-2d+32d=22` {using equation 1}

`30d=21`

`d=(21)/(30)`

d = 0.7

Putting the value of d in equation 1 we get;

`a=1-(2 * 0.7)`

a = 1 - 1.4 = -0.4

Hence, the first term of an AP is -0.4.