If a geometric sequence starts with a first term of 2 and grows exponentially by a factor of 3, what is the sum of the 4th and 5th terms?

1 Answer
Jun 1, 2018

Answer:

#4^(th) term = color(red)(a_4 = a r^(4-1) )= a r^3 = 2 * (2^3)^3 = color(orange)(1024#

#5^(th) term = color(red)(a_5 = a r^(5-1))= ar^4 = 2 * (2^3)^4 = color (orange)( 8172#

Explanation:

#a = 2, r = a^3 = 2^3#

#a_2 = a r = 2 * 2^2 = 16#

#color(red)(a_4 = a r^(4-1) )= a r^3 = 2 * (2^3)^3 = color(orange)(1024#

#color(red)(a_5 = a r^(5-1))= 2 * (2^3)^4 = color (orange)( 8172#