The geometric series with 4th term as 10 and 7th term as 80 has the sum of the first tenth terms as 1278.75.
aₙ = arⁿ⁻¹
where
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
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