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A level maths sum to infinity series help!

The question is:

The nth term of a geometric sequence is Un=r^n
Sum to infinity is 5
Find the value of r

So i did:
S(infinity)=a/1-r
5=1/1-r
5-5r=1
5r=4
r=4/5

But the answer says that it is 5/6. I'm confused. I was thinking maybe a does not =1, but I don't know what else it could be = to. I think it is possible I have made a very silly basic error, but I just cannot see what I have done wrong. Please help!

Reply 1

Original post
by JimMiller069
The question is:
The nth term of a geometric sequence is Un=r^n
Sum to infinity is 5
Find the value of r
So i did:
S(infinity)=a/1-r
5=1/1-r
5-5r=1
5r=4
r=4/5
But the answer says that it is 5/6. I'm confused. I was thinking maybe a does not =1, but I don't know what else it could be = to. I think it is possible I have made a very silly basic error, but I just cannot see what I have done wrong. Please help!

Have you posted the exact question? Could they be starting at n = 0 or n = 1? Has this come from a textbook or an exam paper?

Reply 2

Original post
by JimMiller069
The question is:
The nth term of a geometric sequence is Un=r^n
Sum to infinity is 5
Find the value of r
So i did:
S(infinity)=a/1-r
5=1/1-r
5-5r=1
5r=4
r=4/5
But the answer says that it is 5/6. I'm confused. I was thinking maybe a does not =1, but I don't know what else it could be = to. I think it is possible I have made a very silly basic error, but I just cannot see what I have done wrong. Please help!

a is not equal to 1. from the expression Un=r^n, the first term occurs when n=1, thus first term (a) = r. from there, ull get r = 5/6

usually, Un is expressed in terms of ar^(n-1), which was the 'trick' in the qn
(edited 1 year ago)

Reply 3

Original post
by davros
Have you posted the exact question? Could they be starting at n = 0 or n = 1? Has this come from a textbook or an exam paper?
It is from the Cambridge A Level Mathematics for AQA Student Book 2

Reply 4

Original post
by helloos
a is not equal to 1. from the expression Un=r^n, the first term occurs when n=1, thus first term (a) = r. from there, ull get r = 5/6
usually, Un is expressed in terms of ar^(n-1), which was the 'trick' in the qn

Thank you! I understand the question now! 😃

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