C1 sequences and series question Watch

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*girlie*
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#1
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16) Each year, for 40 years, Anne will pay money into a savings scheme. In the first year she pays in £500. Her payments then increase by £50 each year, so that she pays in £550 in the second year, £600 in the third year, and so on.
a) Find the amount that Anne will pay in the 40th year.
b) Find the total amount that Anne will pay in over the 40 years. (just like any other sum, right? Since you know n, a, and d)
c) Over the same 40 years, Brian will also pay money into the savings scheme. In the first year he pays in £890 and his payments then increase by £d each year. Given that Brian and Anne will pay in exactly the same amount over the 40 years, find the value of d.

I need help mostly with a) and c). You just use the S_n formula for b, right?
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Cortez
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For part A, its an arithmetic series and you want to find the nth term, where n = 40.

nth term in an AP = a + (n - 1)d

a = first value which is £500
n = 40
d = common difference which is 50

So, 500 + (40-1)*50 = 500 + 1950 = £2450

I'm pretty sure thats right. With part B you do use the sum to n formula. Part C is a little tricky, someone else can help with that :p:

Hope it helps ya
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*girlie*
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Ahh, i see. Thanks for helping me out! So, can anybody help me with part c??
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Eye
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For part c) I think you make the two Sn's equal when n=40

EDIT - Wrong formula
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Chewwy
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#5
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(Original post by Blobga)
890 +39d =2450
that gives d = 40, which is incorrect.

b)

Sn = (n/2)(2a + (n-1)d)
=20(1000 + 50(39))
= 59000

c)

59000 = (40/2)(2(890) + 39d)
...
d = ((59000/20) - 1780) / 39
= 30
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Eye
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#6
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Oops yeah sorry I'm mixing up my nth terms and Sums to nth terms.
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