Question

A. Find the A.P. in which (a) T_n = 2n + 1 (b) T_n = 4 − 5n (c) S_n = 5n² + 3n

B. (a) In an A.P. the fourth and seventh terms are 17 and 23 respectively, find ‘d’ and ‘a’.

(b) In and A.P. T₁₀ = 20 and T₂₀ = 10 find T₃₀

(c) The fifth and tenth terms are in the ratio 1 : 2 and T₁₂ = 36 find A.P.

Answer 1

(A)

(a)

∴ and

Hence, the A.P. is

(b)

∴ and

Hence, the A.P. is

(c)

∴and .

Hence, the A.P. is 8, 18, 28, 38 …

(B)

(a) It is given that 17 and 23.

Subtracting equation (1) from equation (2):

Substituting in (1), we get:

(b) It is given that and .

Subtracting equation (1) from equation (2), we get:

Substituting in (1), we get:

(c) It is given that= 1 : 2 and .

Also,

Thus, the required A.P. is 3, 6, 9, 12 …