The 5 th , 8 th and 11 th terms of a G.P. are p , q and s , respectively. Show that q 2 = ps .
5 t h , 8 t h and 11 t h terms of the G.P. are p , q and s respectively.
Let the first term and common ratio of the given G.P. be a and r respectively.
The formula for n t h term of a G.P. is given by,
a n = a r n − 1 (1)
Substitute the values of a and r in equation (1) to obtain the corresponding terms.
a 5 = a × ( r ) 5 − 1 p = a r 4 (2)
a 8 = a × ( r ) 8 − 1 q = a r 7 (3)
a 11 = a × ( r ) 11 − 1 s = a × ( r ) 10 (4)
Divide equation (2) by equation (1).
a r 7 a r 4 = q p r 3 = q p (5)
Divide equation (3) by equation (2).
a r 10 a r 7 = s q r 3 = s q (5)
Equate the values of r 3 obtained in equation (4) and equation (5).
q p = s q q 2 = p s
Hence, it is proved that q 2 = p s .
Let the first term and common ratio of the given G.P. be
The formula for
Substitute the values of
Divide equation (2) by equation (1).
Divide equation (3) by equation (2).
Equate the values of
Hence, it is proved that
