Question

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

Answer 1

Answer:

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Here, a = 21,

d = 18 – 21 = – 3

and

an = – 81, and we have to find n.

As an = 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.

Next, we want to know if there is any n for which an = 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.

Answer 2

Here, a = 21,

d = 18 – 21 = – 3

and

an = – 81, and we have to find n.

As an = 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.

Next, we want to know if there is any n for which an = 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.