Question

The common ratio in a geometric series is 0.5 and the first term is 256. find the sum of the first 6 terms in the series.

A) 256.75
B) 260.875
C) 255.9375
D) 253.96875

Answer 1

To find the sum of the first 6 terms in a geometric series with a common ratio of 0.5 and a first term of 256, use the formula for the sum of a geometric series. Substitute the given values into the formula and calculate the sum.

Step-by-step explanation:

To find the sum of the first 6 terms in the geometric series with a common ratio of 0.5 and a first term of 256, 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.

1. Substituting the given values, we get S = 256 * (1 - 0.5^6) / (1 - 0.5)
2. Calculating the exponent: 0.5^6 = 0.015625
3. Simplifying the equation: S = 256 * (1 - 0.015625) / 0.5
4. Reducing the equation: S = 256 * 0.984375 / 0.5
5. Solving for S: S = 500 / 0.5
6. Calculating the sum: S = 1000

Therefore, the sum of the first 6 terms in the series is 1000.