Find the 12 th term of a G.P. whose 8 th term is 192 and the common ratio is 2.
The 8 t h term of the G.P. is 192 and common ratio is 2.
The formula for n t h term of a G.P. is given by,
a n = a r n − 1 (1)
Let the first term and common ratio of the given G.P. be a and r respectively.
r = 2 a 8 = 192
Substitute the values of a 8 and r in equation (1) to obtain a .
a 8 = a × ( 2 ) 8 − 1 192 = a × ( 2 ) 7 a = 192 128 a = 3 2
Similarly, substitute the values of a and r in equation (1) to obtain the 12 t h term.
a 12 = 3 2 × ( 2 ) 12 − 1 = 3 2 × ( 2 ) 11 = 3 × ( 2 ) 10 = 3072
Thus, the 12 t h term of the G.P. is 3072 .
The
The formula for
Let the first term and common ratio of the given G.P. be
Substitute the values of
Similarly, substitute the values of
Thus, the
