Question

The first term of a G.P. is –3. If the 4th term of this G.P. is the square of the 2nd term, then find its 7th term.

Answer 1

a = −3

n^th term for a G.P. `a_n = ar^(n - 1)`

a₄ = (a₂)²

ar³ = (ar)²

-3r³ = 9r²

r = `9/-3`

r = −3

7^th term for a G.P.

a₇ = ar⁶

= (−3)(−3)⁶

a₇ = (−3)⁷

a₇ = 2187