Question

What is the sum of the first 5 terms of a geometric series with a sub 1 = 10 and r = 1/5?

Answer 1

Answer:

12.496

Step-by-step explanation:

a=10 (first term)

r= 1/5 (common ratio)

sum of first five terms

$s_{5} = \frac{a( 1 - {r}^{n} ) }{1- r}$

=10{1-⅕⁵} ÷ 1-⅕

=10{1 - 1/3125} ÷ 4/5

=10{3124/3125} ÷ 4/5

=9.9968÷0.8

=12.496.

OR

a+ar+ar²+ar³+ar⁴

=10+(10x⅕)+(10x⅕²)+(10x⅕³)+(10x⅕⁴)

=10+2+0.4+0.08+0.016

=12+0.48+0.016

=12.496

Answer 2

Answer:

a 1 = 10

a 2 = 10 * 1/5 = 2

a 3 = 2 * 1/5 = 2/5

a 4 = 2/5 * 1/5 = 2/25

a 5 = 2/25 * 1/5 = 2/125

S 5 = a 1 + a 2 + a 3 +a 4 + a 5= 10 + 2 + 2/5 + 2/25 + 2/125 =

= 1250/125 + 250/125 + 50/125 + 10/125 + 2/125 =  1562 / 125