Question

In an arithmetic progression (AP), the 9th term is 5 times the 2nd term and the 8th term is 1 more than 10 times the first term. What is the 4th term of the geometric progression (GP) whose first term is the second term of AP and whose common ratio is equal to the common difference of AP?
A. 1792

B. 448

C. 192

D. 576​

Answer 1

Answer:

c is the ans ok hope this was helpful to you

Answer 2

Solution :-

Let first term of AP is a and common difference is d .

so,

→ 9th term = 5 * 2nd term

→ a + 8d = 5(a + d)

→ a + 8d = 5a + 5d

→ 8d - 5d = 5a - a

→ 3d = 4a

→ d = (4a/3) ----------- Eqn.(1)

now,

→ 8th term = 10 * first term + 1

→ a + 7d = 10a + 1

→ 7d = 9a + 1

putting value of d from Eqn.(1),

→ 7(4a/3) = 9a + 1

→ 28a = 27a + 3

→ 28a - 27a = 3

→ a = 3 .

putting value of a in Eqn.(1),

→ d = (4 * 3)/3

→ d = 4 .

then,

→ 2nd term of AP = a + d = 3 + 4 = 7 = first term of GP .

→ common ratio of GP = d = 4 .

therefore,

→ Tn = ar^(n-1)

→ T(4) = 7 * 4^(4 - 1)

→ T(4) = 7 * 4³

→ T(4) = 7 * 64

→ T(4) = 448 (B) (Ans.)

Hence, 4th term of GP will be 448 .