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

Answer:

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

$a,ar^{1} ,ar^{2} ,ar^{3} .....$

$T_{n}=ar^{n-1}$

$T_{1}=ar^{0}=a=256\\T_{2}=ar^{1}=a\times r=256\times 0.5=128\\T_{3}=ar^{2}=a\times r^{2}=256\times 0.5^{2}=64\\T_{4}=ar^{3}=a\times r^{3}=256\times 0.5^{3}=32\\ T_{5}=ar^{4}=a\times r^4=256\times 0.5^4 =16\\T_{6}=ar^{5}=a\times r^5 =256\times 0.5^5=8$