CBSE Class 10 Answered

(1)

a_n= 3+2n

Now, put n=1,2,3,...

a₁= 3+2(1) = 5

a₂= 3+2(2) = 7

a₃= 3+2(3) = 9

Thus, the terms of the AP are 5,7,9,....

Here, a = 5 and d = 2

S₂₄= [25+(24 -1)2]

= 12[10+46]

= 12  56

= 672

(2)

In the first AP, a = 63 and d = 2

In the second AP, a = 3 and d = 7

As the nth term of both APs be equal

63+(n-1)2 = 3+(n-1)7

63+2n-2 = 3+7n-7

61+2n = 7n-4

5n = 65

n = 13

Hence, the 13th term of the APs are equal.

3)

pth term is a and qth term is b

A + (p - 1)D = a  ... (1)

A + (q - 1)D = b  ... (2)

Subtracting (2) from (1), we get

(p-1-q+1)D = a-b

D = a-b/p-q

Adding (1) and (2), we get

2A + D(p+q-2) = a+b

2A + D(p+q-1) = a+b+D