For the series 16, 24, 36, 54,... find S7.
A) 32.17
B) 115.75
C) 514.75
D) 3906.25
B?
To find the sum of the series 16, 24, 36, 54,... we need to first identify the common difference. From the given series, we can observe that each term is obtained by multiplying the previous term by 1.5.
So, the sequence can be written as 16, 24, 36, 54, 81, 121.5, ...
We can use the formula for the sum of a geometric series to find the sum, given by:
Sn = a * (r^n - 1) / (r - 1)
where Sn is the sum of the first n terms, a is the first term, r is the common ratio, and n is the number of terms.
In this case, a = 16 (the first term), r = 1.5 (the common ratio), and n = 7 (the number of terms we want to find the sum for).
Plugging the values into the formula, we get:
S7 = 16 * (1.5^7 - 1) / (1.5 - 1)
Calculating this expression, we get:
S7 = 514.75
Therefore, the sum of the first 7 terms of the series is 514.75.
So, the correct option is:
C) 514.75
To find the sum of a series, we need to first determine the pattern or rule that governs the series, and then use that rule to calculate the sum.
Looking at the given series 16, 24, 36, 54, ..., we can see that each term is obtained by multiplying the previous term by 1.5.
To calculate the sum of the series, we can use the formula for the sum of a geometric series:
S = a * (1 - r^n) / (1 - r),
where S is the sum of the series, a is the first term, r is the common ratio, and n is the number of terms.
In this case, the first term (a) is 16, the common ratio (r) is 1.5, and we need to find the sum up to the 7th term (n = 7).
Plugging these values into the formula, we get:
S = 16 * (1 - 1.5^7) / (1 - 1.5).
Calculating this gives us:
S = 16 * (1 - 8.5) / (-0.5) = 16 * (-7.5) / (-0.5) = 120.
Therefore, the sum of the given series up to the 7th term is 120.
None of the provided answer choices match the correct value of 120, so none of the options A, B, C, or D are correct.
looks like a GP with a = 16, and r = 3/2
sum(7) = a( r^7 - 1)/(r-1)
= 16(2187/128) - 1)/(1/2)
= 32(2059/128)
= 2059/4 or 514.75
how can the answer be 115.75 when the first 4 terms shown already add up to 130 ?
Are you just guessing ?