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# Sequences and series C1 watch

1. Please could anyone help me with some questions, this topic is really confusing me Thanks!

The first term of an arithmetic sequence is 30 and the common difference is -1.5.

Find the 25hth term, I got -6, is that right?

Then the rth term of the sequence is 0, find the value of r. Would I just set the Un = a+(n-1)d as 0 = 30+(r-1)-1.5 so r=21? Can anyone please explain if this is right and if not why and what to do?

Next, it says 'Alice receives an allowance of £500 on her 11th birthday, every year after it inc by £200. When the total allowance Alice has received is £3200, it stops. Find the age at which this happens.

So I did the Sn formula to get n=4 but then I don't know what to do? Could anyone please explain this too? Thanks!
2. (Original post by Qaiys)
Please could anyone help me with some questions, this topic is really confusing me Thanks!

The first term of an arithmetic sequence is 30 and the common difference is -1.5.

Find the 25hth term, I got -6, is that right?
Yes.

Then the rth term of the sequence is 0, find the value of r. Would I just set the Un = a+(n-1)d as 0 = 30+(r-1)-1.5 so r=21? Can anyone please explain if this is right and if not why and what to do?
That's correct. As a check you could work out what the 21st term is.

Next, it says 'Alice receives an allowance of £500 on her 11th birthday, every year after it inc by £200. When the total allowance Alice has received is £3200, it stops. Find the age at which this happens.

So I did the Sn formula to get n=4 but then I don't know what to do? Could anyone please explain this too? Thanks!
So, she receives 4 allowances. Since she got her first one on her 11th birthday, and gets 1 a year, her age when she receives the fourth will be....
3. (Original post by ghostwalker)
Yes.

That's correct. As a check you could work out what the 21st term is.

So, she receives 4 allowances. Since she got her first one on her 11th birthday, and gets 1 a year, her age when she receives the fourth will be....
Thank you! And 14? :P
4. (Original post by Qaiys)
Thank you! And 14? :P
Yep.
5. (Original post by ghostwalker)
Yep.
Thank you!

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