Mathematics

The fourth term of a G.P. is the square of its second term and the first term is -3. Find its 7th term.

28 Likes

Given, a₄ = (a₂)² and a = -3.

a_n = ar^{n - 1}
∴ a₄ = ar³ and a₂ = ar.

Since, a₄ = (a₂)²
∴ ar³ = (ar)²
⇒ (-3)r³ = (-3r)²
⇒ -3r³ = 9r²
⇒ 9r² + 3r³ = 0
⇒ r²(9 + 3r) = 0
⇒ r² = 0 or 9 + 3r = 0
⇒ r = 0 or r = -3.

As common ratio cannot be equal to zero so, r ≠ 0.

a₇ = ar⁶ = (-3)(-3)⁶ = -3 × 729 = -2187.

Hence, the 7th term of the G.P. is -2187.

Answered By

13 Likes