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The 6th term of a GP is 2000. Find its first term if its common ratio is 10Asked by Maryam
The 6th term of a gp is 2000.find the first term if its common ratio is 10
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Answered by
Bosnian
In GP n-th term is:
an = a • r ⁿ⁻¹
where
a = a1 = the first term
r = common ratio
In this case:
n = 6
a6 = 2,000
r = 10
a6 = a • r ⁵
2,000 = a • 10 ⁵
2,000 = a • 100,000
100,000 a = 2,000
a = 2,000 / 100,000
a = 0.02
a1 = a = 0.02
an = a • r ⁿ⁻¹
where
a = a1 = the first term
r = common ratio
In this case:
n = 6
a6 = 2,000
r = 10
a6 = a • r ⁵
2,000 = a • 10 ⁵
2,000 = a • 100,000
100,000 a = 2,000
a = 2,000 / 100,000
a = 0.02
a1 = a = 0.02