Question

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

Answer 1

4 th term of the G.P. is square of its second term. Also the first term is −3.

Let the first term and common ratio of the given G.P. be a and r respectively.

The formula for n th term of a G.P. is given by,

a n =a r n−1 (1)

Here, a=−3.

Substitute the values of a and r in equation (1) to obtain the corresponding terms.

a 4 =a× ( r ) 4−1 =a r 3 (2)

a 2 =a× ( r ) 2−1 =ar (3)

As per the given condition,

( a 2 ) 2 = a 4 (4)

Substitute the values of a 2 and a 4 from equation (2) and equation (3) in equation (4).

a r 3 = ( ar ) 2 a r 3 = a 2 r 2

Substitute the value of a in the above expression.

−3 r 3 = ( −3 ) 2 r 2 −3r=9 r=−3

Substitute the values of a and r in equation (1) to obtain the seventh term.

a 7 =a r 7−1 =−3× ( −3 ) 6 =−2187

Thus, the seventh term of the G.P. is −2187.