Question :

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

Mathematics

Class 11

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Aanya

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

As a= 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= 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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