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Find the sum of first 20 terms of GP with first term of 3 and common ratio 1.5?
Awa Kals
Mar 26
Find the sum of first 20 terms of GP with first term of 3 and common ratio 1.5?
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ChatGPT
Mar 26
To find the sum of the first 20 terms of a geometric progression (GP) with a first term of 3 and a common ratio of 1.5, we can use the formula for the sum of the first n terms of a GP:
Sum of n terms = a * (1 - r^n) / (1 - r)
Where:
a = first term = 3
r = common ratio = 1.5
n = number of terms = 20
Plugging in the values, we get:
Sum of 20 terms = 3 * (1 - 1.5^20) / (1 - 1.5)
Sum of 20 terms = 3 * (1 - 3,435,973.5) / (-0.5)
Sum of 20 terms = 3 * (-3,435,972.5) / (-0.5)
Sum of 20 terms = -10,307,917.5 / -0.5
Sum of 20 terms = 20,615,835
Therefore, the sum of the first 20 terms of the given GP is 20,615,835.
Sum of n terms = a * (1 - r^n) / (1 - r)
Where:
a = first term = 3
r = common ratio = 1.5
n = number of terms = 20
Plugging in the values, we get:
Sum of 20 terms = 3 * (1 - 1.5^20) / (1 - 1.5)
Sum of 20 terms = 3 * (1 - 3,435,973.5) / (-0.5)
Sum of 20 terms = 3 * (-3,435,972.5) / (-0.5)
Sum of 20 terms = -10,307,917.5 / -0.5
Sum of 20 terms = 20,615,835
Therefore, the sum of the first 20 terms of the given GP is 20,615,835.
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