Question

Find a for the given geometric series.

S = 45450, r = 3.6, n = 6

Answer 1

ok here's an example: Find a1 for the geometric series in which Sn=105, r=-2, n=6

Sum of the first n terms of a geometric series is:
S = a*(1 - r^n)/(1 - r)

Here a is the first term of the series and r is the common ratio.
Plugging in the values that you have been given:

105 = a*(1 - (-2)^6)/(1 - (-2))
=> 105 = a*(1 - 64)/3
=> 105 = a*(-63)/3
=> 105 = -21a
=> a = -5

Hence first term a = -5.

3) Find the sum of the geometric series in which a1= 256, an=81 r=3/4

nth term of a geometric sequence is:

a(n) = a*r^(n - 1)

where a(n) = nth term
a = first term
r = common ratio
n = number of terms

Using the given values in the equation, we have:

81 = 256*(3/4)^(n - 1)
=> 81/256 = (3/4)^(n - 1)
=> (3/4)^4 = (3/4)^(n - 1)
=> 4 = n - 1
=> n = 5

Now, sum of the first n terms of a geometric series is:
S = a*(1 - r^n)/(1 - r)

we know that n = 5 here. Using the remaining values, we have:

S = 256*(1 - (3/4)^5)/(1 - 3/4)
=> S = 256*(1 - 243/1024)/(1/4)
=> S = 256*(781/1024)*4
=> S = 781
Go with this and see if you can get it if not give me a buzz