Question

Which term of AP 21 , 18, 15, ............. is -81 ?also is an term 0 Give reason for your answer ??????

Answer 1

Given:

The first term of the AP (a) = 21

Calculating the common difference of the AP (d)

= 18 - 21

= - 3

The formula to find the nth term of an AP:

An = a + (n - 1) d

Substituting all the values which we know into this formula:

– 81 = 21 + (n – 1)(– 3)

– 81 = 24 – 3n

– 105 = – 3n

n = - 105 / - 3

n = 35

Hence, the 35 th term of the AP is - 81.

We need to check if there is any n for which an = 0

Checking if any term is 0:

21 + (n – 1) (–3) = 0

21 - 3n + 3 = 0

24 - 3n = 0

3(8 - n) = 0

(8 - n) = 0 / 3

8 - n = 0

Taking n to the other side of the equation we get:

n = 8

Therefore, the eighth term of the AP is Zero.