Question

The first term of A.P is 5 and the last term is 45 and the sum of all term is 400. find the number of terms and the Common difference.

help me plz ​

Answer 1

`n =16` --- Number of terms

`d = (8)/(3)` --- Common difference

Step-by-step explanation:

Given

`a = 5` --- first term

`T_n = 45`

`S_n = 400`

Required

Determine the number of terms (n) and the common difference (d)

The sum of n terms of an AP is:

`S_n = (n)/(2)(a + T_n)`

This gives:

`400 = (n)/(2)(5 + 45)`

`400 = (n)/(2) * 50`

`400 = n * 25`

Divide both sides by 25

`16 = n`

`n =16`

The nth term of an AP is:

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

This gives:

`45 = 5 + (16 - 1) * d`

`45 = 5 + 15 * d`

Subtract 5 from both sides

`45 - 5= 5 - 5 + 15 * d`

`40= 15 * d`

Divide both sides by 15

`(40)/(15) = d`

`(8)/(3) = d`

`d = (8)/(3)`