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Find the sum of this geometric series

Find the sum of this geometric series-example-1
User Odile
by
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1 Answer

4 votes

Answer:

S₆ = 39060

Explanation:

the sum of a finite geometric sequence is


(a_(1)(r^(n)-1) )/(r-1)

where a₁ is the first term and r the common ratio

the expression inside the ∑ is not in this form

so we require to find a₁ and r

the common ratio r =
(a_(n+1) )/(a_(n) ) , then

r =
(2(5^(n+1)) )/(2(5^(n)) ) ← cancel 2 on numerator/ denominator

=
(5^(n+1) )/(5^(n) )

=
(5^(n)(5) )/(5^(n) ) ← cancel
5^(n) on numerator/ denominator

= 5

find first term in series a₁ by substituting in the lower bound and simplifying.

a₁ = 2
(5)^(1) = 2 × 5 = 10

now substitute a₁ = 10 and r = 5 into the sum formula


(10(5^(6)-1) )/(5-1)

=
(10(15625-1))/(4)

=
(10(15624))/(4)

=
(156240)/(4)

= 39060

User Mattarau
by
8.6k points

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