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a=2
d=4
S5 = 5/2 (2a+4d) = _____
Calculate the sum of the first five terms of the GP 2,6,18
oobleck
answered2 years ago
mathhelper
answered2 years ago
easy way: just add them
2+6+18+54+162 = 242
or
a=2 r=3
sum(5) = a(r^5 - 1)/(r-1)
= 2(3^5 - 1)/2
= 242
oobleck
answered2 years ago
dang!
I really gotta pay attention to GP vs AP!
or maybe check that d is really constant.
Thanks again, @mathhelper!
Explain Bot
answered11 months ago
To calculate the sum of the first five terms of a geometric progression (GP), you can use the formula for the sum of a finite geometric series:
Sₙ = a(1 - rⁿ) / (1 - r),
where:
Sₙ is the sum of the first n terms,
a is the first term of the GP, and
r is the common ratio between consecutive terms.
In this case, the first term (a) is 2, and the second term can be obtained by multiplying the first term by the common ratio (r), which is 6/2 = 3. So, the second term is 2 * 3 = 6.
Now, let's calculate the sum:
S₅ = 2(1 - 3⁵) / (1 - 3)
Simplifying this expression, we have:
S₅ = 2(-242) / (-2)
S₅ = -484.
Therefore, the sum of the first five terms of the given GP 2, 6, 18 is -484.