Find the 20 th and n th terms of the G.P.
The given G.P. is 5 2 , 5 4 , 5 8 , …
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.
a = 5 2 r = 1 2
Substitute the values of a and r in equation (1) to obtain the 20 t h term.
a 20 = 5 2 × ( 1 2 ) 20 − 1 = 5 2 × ( 1 2 ) 19 = 5 2 20
Similarly, substitute the values of a and r in equation (1) to obtain the n t h term.
a n = 5 2 × ( 1 2 ) n − 1 = 5 2 × 2 n − 1 = 5 2 n
Thus, the first and n t h term of the G.P. is 5 2 20 and 5 2 n respectively.
The given G.P. is
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 first and
