I need some assistance or a formula when trying to find the first term of geometric series please! I don't understand this!!!!
What is the first term of a geometric series with a summation of 289, 5 terms and a common ratio of 1/2?
g + g r + g r^2 + g r^3 + g r^4 = 289
g (1 + 1/2 + 1/4 + 1/8 + 1/16) = 289
find sum of
1 + 1/2 + 1/4 + 1/ 8 + 1/16
S5 = [1-(1/2)^5]/(1/2) = 31/16
so
g (31/16) = 289
g = 149.16
Thank you Damon, that helped alot...
To find the first term of a geometric series, you can use the formula:
First Term (a) = Summation (S) / (Number of terms (n) * Common Ratio (r)^(n-1))
In this case, you are given:
Summation (S) = 289
Number of terms (n) = 5
Common Ratio (r) = 1/2
Let's substitute these values into the formula:
First Term (a) = 289 / (5 * (1/2)^(5-1))
= 289 / (5 * (1/2)^4)
= 289 / (5 * (1/16))
= 289 / (5/16))
To divide by a fraction, we invert the divisor and multiply:
= 289 * (16/5)
= 462.4
So, the first term of the geometric series is 462.4.