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A man saves $ 4 more each year than the preceding year. If

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A man saves $ 4 more each year than the preceding year. If [#permalink] New post 28 Nov 2005, 03:10
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A man saves $ 4 more each year than the preceding year. If he saves Rs 20 in the first year, after how many years will his savings amount to $1064?
a) 10
b) 12
c) 18
d) 19
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 [#permalink] New post 28 Nov 2005, 04:38
A man saves $ 4 more each year than the preceding year. If he saves Rs 20 in the first year, after how many years will his savings amount to $1064?

A(n) = A(n-1) + 4

A(1) = 20
A(2) = 20 + 4
A(3) = 20 + 4 + 4
A(4) = 20 + 4 + 4 + 4
.
.
.
A(N) = 20 + 4(N - 1)

A(1) + A(2) + A(3) + A(4) + ... + A(N)
= (20 * N) + 4(0 + 1 + 2 + 3 + ... + N-1)
= (20 * N) + 4( (N-1)N/2 )
= (20 * N) + 2(N^2) - 2N
= 2(N^2) + 18N
= 1064

N^2 + 9N = 532
N^2 + 9N - 532 = 0
(N-19)(N+28)=0

N=19 or N=-28

A year must be positive.

Thus, he needs to save for 19 years.

(E) it is.
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  [#permalink] 28 Nov 2005, 04:38
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