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The fourth term of a geometric series is 10 and the seventh term of the series is 80. Find the sum to 10 terms of the series.

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89 cents Montgomery
Answer:

The geometric series with 4th term as 10 and 7th term as 80 has the sum of the first tenth terms as1278.75.

How to find sum of terms in geometric series?

aₙ = arⁿ⁻¹

where

  • a = first term
  • r = common ratio
  • n = number of terms

Therefore,

10 = ar³

80 = ar⁶

Hence,

a = 10 / r³

80 = (10 / r₃) r⁶

80 = 10r³

r³ = 80 / 10

r = ∛8

r = 2

a = 10 / 2³

a = 10 / 8 = 5 / 4

The sum of 10 terms can be calculated as follows:

Sₙ = a(rⁿ - 1) / r - 1

Sₙ = 5 / 4 (2¹⁰ - 1) / 2 - 1

Sₙ = 5 / 4 (1024 - 1) / 1

Sₙ = 1.25(1023)

Sₙ = 1278.75

learn more on geometric series here:

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