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If The Second Differences Of A Sequence Are A Constant Of 5, The First Of The First Differences Is 9, And Their First Term Is 4, Which Are The First Five Terms Of Sequence?

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Oddman Profile
Oddman answered
If the second differences are a constant = 5, then the series of first differences is
9 14 19 24 29 34 ...

If the first series number is 4, then the series of interest is
4, (4+9)=13, (13+14)=27, (27+19)=46, (46+24)=70, ...

Your series is
4, 13, 27, 46, 70, ...

A series with a first term (N=1) of x1, initial first difference of d1, initial second difference of d2, initial 3rd difference of d3, etc. will have this equation for the Nth term:
xN = x1 + d1(N-1) + d2(N-1)(N-2)/2 + d3(N-1)(N-2)(N-3)/(2*3)

As you can see, this describes a polynomial series. An arithmetic series will have d2=0. A geometric series will have an infinite number of non-zero Nth differences.

Your series has x1=4, d1=9, d2=5, d3=0, so the Nth value in the series is
 xN=4 + 9(N-1) + 5(N-1)(N-2)/2 = 4 + (N-1)(9 + 5(N-2)/2)

Then
 x5 = 4 + 9(5-1) + 5(5-1)(5-2)/2 = 4 + 9(4) + 5(4)(3)/2
 = 4 + 36 + 30 = 70
Anonymous Profile
Anonymous answered
If the second difference of a sequence are a constant 2, the first of the first differences is 10, and the first term is 5, which are the first terms of the sequence?
Anonymous Profile
Anonymous answered
The first term of the sequence is 4
The difference is between first two term is 9

second term 4+9=13

after second the difference is constant 5

Third term = 13 +5 =18

Fouth term = 18 + 5 =23

Fifth term = 23+5 = 28

The numbers are 4, 13, 18, 23,28 >>Answer

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Anonymous