What is the sum of the first 5 terms of a geometric series with a sub 1 = 10 and r = 1/5?
2 answers:
Answer:
12.496
Step-by-step explanation:
a=10 (first term)
r= 1/5 (common ratio)
sum of first five terms
=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:
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 = <u> 1562 / 125</u>
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