Question

The common ratio in a geometric series is 0.50, and the first term is 256. find the first 6 terms in the series.

Im pretty confused on the equation to solve this... a hand please?

Answer 1

To find the first 6 terms in a geometric series, multiply the first term by the common ratio raised to the power of n-1.

Step-by-step explanation:

To find the first 6 terms in a geometric series, we need to multiply the first term by the common ratio raised to the power of n-1, where n is the term number. In this case, the first term is 256 and the common ratio is 0.50. So the first 6 terms would be:

1. 256
2. 256 * 0.50 = 128
3. 128 * 0.50 = 64
4. 64 * 0.50 = 32
5. 32 * 0.50 = 16
6. 16 * 0.50 = 8

Answer 2

256,128,64,32,16,8

Step-by-step explanation:

Given the common ratio(r) = 0.5 and the first term (a)=256

We know that the geometric series with the first term as a and the common ratio as r is

`a,ar^(1) ,ar^(2) ,ar^(3) .....`

`T_(n)=ar^(n-1)`

`T_(1)=ar^(0)=a=256\\T_(2)=ar^(1)=a* r=256* 0.5=128\\T_(3)=ar^(2)=a* r^(2)=256* 0.5^(2)=64\\T_(4)=ar^(3)=a* r^(3)=256* 0.5^(3)=32\\ T_(5)=ar^(4)=a* r^4=256* 0.5^4 =16\\T_(6)=ar^(5)=a* r^5 =256* 0.5^5=8`