Which term of the AP: 21, 18, 15, . . . is – 81? Also, is any term 0? Give reason for your answer.

Maths

Class 10

1071

Aarohi

Aanya

Answer / Solution

Answer / Solution

Solution : Here, a = 21, d = 18 – 21 = – 3 and a_{n} = –81, and we have to find n.

As a_{n }= a + ( n – 1) d, we have;

– 81 = 21 + (n – 1)(– 3)

– 81 = 24 – 3n

– 105 = – 3n

So, n = 35

Therefore, the 35th term of the given AP is – 81. and next, we want to know if there is any n for which a_{n }= 0.

If such an n is there, then;

21 + (n – 1) (–3) = 0,

3(n – 1) = 21

n = 8

Therefore, the eighth term is 0.

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