Question

In and A.P

A. (a) If a = 11, d = 2, n = 10 find T₁₀ and S₁₀

(b) If a = 12, d = 3, T_n = 84 find n

(c) If d = 4 and T₃₅ = 123 find a

(d) If a = 3 and T₂₀ = 60 find d

B. (i) How many terms are there in A.P. 4, −1, −6, ………, (−106)

(ii) Test whether 25 is a term of the A.P. 3, 6, 9, 12, 15, …….

(iii) Test whether 36 is a term of the A.P. 4, 8, 12, 16, …….

Answer 1

(A) It is known that in an A.P.,

(a)

To find: and

(b)

To find: n

(c)

To find: a

(d)

To find: d

(B)

(i)

For this A.P., ,

Let the number of terms in the A.P. be n.

(ii)

For this A.P., ,

Let 25 be the n^th term of this A.P.

Then,

Clearly, n is not a natural number.

Hence, 25 is not a term of this A.P.

iii)

For this A.P., ,

Let 36 be the n^th term of this A.P.

Then,

Here, n is a natural number.

Hence, 36 is a term of this A.P.