Question

the sum of the first three terms of a sequence Is 42 The fourth term is 24. find u1 and the common difference

Answer 1

`10=2d`

Given:

The sum of the first three terms of a sequence Is 42.

The fourth term is 24.

To find:

The u₁ and the common difference

Explanation:

nth term of a sequence is

`u_n=u_1+(n-1)d`

where, u₁ is first term and d is common difference.

4th term is 24.

`u_4=u_1+(4-1)d`

`24=u_1+3d` ...(i)

Sum of nth term of an AP is

`S_n=(n)/(2)[2u_1+(n-1)d]`

Sum of first three terms is 42.

`S_3=(3)/(2)[2u_1+(3-1)d]`

`42=(3)/(2)[2u_1+2d]`

Divide both sides by 3.

`14=u_1+d` ...(ii)

On subtract (ii) from (i), we get

`10=2d`

`5=d`

Put d=5 in equation (ii).

`14=u_1+5`

`14-5=u_1`

`9=u_1`

Therefore, the first term is
`u_1=9` and common difference is
`d=5` .