Question

In a G.P, a₁=5/9 and a₆= 1525/9.Find its nth term?

A) aₙ = 5/9 × (5/3)ⁿ⁻¹
B) aₙ = 5/9 × (3/5)ⁿ⁻
C) aₙ = 5/9 × (9/5)ⁿ⁻
D) aₙ = 5/9 × (2/3)ⁿ⁻

Answer 1

To find the nth term of a G.P., we can use the formula aₙ = a₁ * r^(n-1), where a₁ is the first term and r is the common ratio. By substituting the given values, we can calculate that the nth term of the given G.P. is aₙ = 5/9 * (61)^(n-1).

Step-by-step explanation:

To find the nth term of a geometric progression (G.P.), we need to determine the common ratio (r). We can do this by using the formula:

r = (a₆/a₁)^(1/5)

Substituting the given values, we have:

r = (1525/9) / (5/9) = 305/5 = 61

Now, we can use the formula for the nth term of a G.P.:

aₙ = a₁ * r^(n-1)

Substituting the values again, we get:

aₙ = (5/9) * (61)^(n-1)

Therefore, the nth term of the G.P. is aₙ = 5/9 * (61)^(n-1).