A geometric series is the collection of an unlimited number of terms with a fixed ratio between them. The sum of the first seven terms of the series is 249.
A geometric series is the collection of an unlimited number of terms with a fixed ratio between them.
The given series is an geometric series, the details of the series are:
a₁ = 150
r = 60/150 = 0.4
n = 7
The sum of the geometric series is,
S = 150(1-0.4⁶)/(1-0.4)
S = 248.976 ≈ 249
Hence, the sum of the first seven terms of the series is 249.
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Answer:
250
Step-by-step explanation:
The sum of the terms of a geometric series is given by the formula ...
Sn = a1×(1 -r^n)/(1 -r)
sum of n terms for first term a1 and common ratio r.
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The given series has first term a1 = 150, and common ratio r = 60/150 = 2/5. Putting these values into the formula gives a sum of 7 terms that is ...
S7 = 150×(1 -(2/5)^7)/(1 -2/5) = 150((77997/78125)/(3/5))
S7 = 150×(25999/15625) = 249.5904
Rounded to the nearest integer, the sum of the first 7 terms is 250.
