# 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?

Jun 1, 2018

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:

$a = 2 , r = {a}^{3} = {2}^{3}$

${a}_{2} = a r = 2 \cdot {2}^{2} = 16$

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