Question

An AP has a common difference of 2 and a G.P has a common ratio of 3. The corresponding terms are Added together to produce a new sequence. If the first term is 8 and the third term is 52, find the (i) AP and the G.P (ii) the new sequence​

Answer 1

The AP is 48, 50, 52, 54,... and the GP is 52/9, 52/3, 52, 156,... The new sequence is obtained by adding the corresponding terms of the AP and GP.

Step-by-step explanation:

(i) To find the terms of the arithmetic progression (AP), we can use the formula: nth term (Tn) = a + (n-1)d.

Given that the common difference (d) is 2 and the third term (T3) is 52, we can solve for the first term (a):

T3 = a + (3-1)2 = 52

a + 2(2) = 52

a + 4 = 52

a = 52 - 4 = 48

So, the arithmetic progression (AP) is 48, 50, 52, 54,...

To find the terms of the geometric progression (GP), we can use the formula: nth term (Tn) = a * r^(n-1).

Given that the common ratio (r) is 3 and the third term (T3) is 52, we can solve for the first term (a):

T3 = a * 3^(3-1) = 52

a * 3^2 = 52

a * 9 = 52

a = 52 / 9

So, the geometric progression (GP) is 52/9, 52/3, 52, 156,...

(ii) To find the new sequence obtained by adding the corresponding terms of the AP and GP, we add each term of the AP to the corresponding term of the GP.

For example, the first term of the new sequence is 48 + (52/9) = (432 + 52) / 9

= 484 / 9.