The 4th term of a G.P. is square of its 2nd term, and the first term is –3. Determine its 7th term.

Question

Philoid · Accepted Answer

Let a and r be the first term and common ratio respectively.
Then a = -3

4th term = a4 = ar3 = -3r3

2th term = a2 = ar = -3r
a4 = (a2)2

-3r3 = (-3r)2

-3r3 = 9r2

r = -3

7th term = a7 = ar6 = -3(-3)6 = -3(-3)6= (-3)7 = - 2187

The 4^th term of a G.P. is square of its 2^nd term, and the first term is –3. Determine its 7^thterm.