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What is the sum of the first five terms of a geometric series with a1=10 and r=1/5?

Answer 1

Cora Alexander

Sum of first #5# terms is #12.496#

First term #a1=10# , common ratio, #r=1/5=0.2#

number of terms , #n=5#

Sum of first #5# terms is # S_5=(a_1*(1-r^n))/(1-r)# or

# S_5=(10*(1-0.2^5))/(1-0.2)=12.496#

Sum of first #5# terms is #12.496# [Ans]

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Answer 2

Elias Ackerman

The sum of the first five terms of a geometric series with ( a_1 = 10 ) and ( r = \frac{1}{5} ) can be calculated using the formula for the sum of a geometric series:

[ S_n = a_1 \frac{1 - r^n}{1 - r} ]

Substituting the given values:

[ S_5 = 10 \frac{1 - (1/5)^5}{1 - 1/5} ]

[ S_5 = 10 \frac{1 - (1/3125)}{4/5} ]

[ S_5 = 10 \frac{1 - 0.00032}{0.8} ]

[ S_5 = 10 \frac{0.99968}{0.8} ]

[ S_5 = 10 \times 1.2496 ]

[ S_5 = 12.496 ]

Therefore, the sum of the first five terms of the geometric series is ( 12.496 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.