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defon
2 years ago
15

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.

Mathematics
1 answer:
erica [24]2 years ago
5 0

The geometric series with 4th term as 10 and 7th term as 80 has the sum of the first tenth terms as 1278.75.

<h3>How to find sum of terms in geometric series?</h3>

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: brainly.com/question/13592208

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