Given the following geometric sequence: 32, ____, ____,4,.........
Find the missing two terms
find the nth term
find the sum of the first 5 terms
find the sum of all the terms. Explain your answer
Ok based on the given we can observe that the sequence is decreasing by n(1/2). That gives us the complete sequence: 32,16,8,4.
There is a formula for this but it requires two consecutive numbers in a series which is rn=an / an-1
the nth term can be calculated by the formula an=a1r^n-1. We already determined that r=1/2 above. So we just need to plug in our values
an=32* (1/2)^n-1. We can now use this formula to calculate any of the n terms we would like.
Sum of the first 5 terms is done by the formula: Sn=a1 (1-r^n)/1-r
So we plug in our Values:
S5=32(1-1/2^5)/1-1/2 >> S5=32(1-1/32)/.5 >> S5=32(31/32)/.5 S5 = 62
For the last part we use the formula: Sinfinity= a1 /1-r
this formula has a condition though the conditions are "r" must be between -1 & 1 for it to have an infinite series. Since our "r" value was 1/2 we are able to use this.
Sinfinity= 32/1-.5 = 32/.5 = 64
Hope this helps