How do you write the expression for the nth term of the geometric sequence #a_2=3, a_5=3/64, n=1#?

1 Answer
May 17, 2018

Answer:

#color(crimson)(a_n = a_1 = a = 12#

Explanation:

Formula for nth term #a_n = a r^(n-1)#

Given #a_2 = 3, a_5 = 3/64, n = 1#

To find first term ‘a’ as n = 1

#a_2 = a r^(2-1) = a r = 3#

#a_5 = a r^(5-1) = a r^4 = 3/64#

#a_5 / a_2 = (ar^4) / (a r) = r^3 = (cancel3/64)/cancel3 = 1/64#

#r^3 = (1/4^3), r = 1/4#

We know, #a_2 = a r = 3#

#:. a = 3/r = 3/(1/4) = 12#

Hence, #color(crimson)(a_n = a_1 = a = 12#