# Linear nth term explained by 6c8gI7u

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• pg 1
```									   common
difference zero'th      n>
-5 term          1      2      3    4    5       6
-5 n       -3   -8 -13 -18 -23 -28 -33
-5 n       -2   -7 -12 -17 -22 -27 -32
-5 n       -1   -6 -11 -16 -21 -26 -31
-5 n        0   -5 -10 -15 -20 -25 -30
-5 n + 1        -4     -9 -14 -19 -24 -29
-5 n + 2        -3     -8 -13 -18 -23 -28
-5 n + 3        -2     -7 -12 -17 -22 -27
How to tell what the nth term is for a sequence:
1. Sequences always start with n (or input) as number 1, then 2,and so o
2. The common (first) difference between terms is the multiple of n
… i.e. cell A2 is the same as the numbers in column A
… so an increasing sequence is positive n, decreasing is negative n
3. When n is zero (column D), this is the adjustment to the times table to
4. So the nth term is the common difference in the sequence,
… mulitplied by n, and then adjusted up or down.
7     8
-38   -43
-37   -42
-36   -41
-35   -40
-34   -39
-33   -38
-32   -37

number 1, then 2,and so on…
ms is the multiple of n

creasing is negative n
tment to the times table to get the sequence
the sequence,
remember, n = 1        2       3     4      5     6
sequence      (enter it below)
zero'th term = 11 8          5       2     -1     -4    -7
1st difference =          -3    -3      -3     -3    -3    -3
BUT           -3 n = -3      -6      -9    -12 -15 -18
so, nth term =      -3 n + 11
7

-10
hence    -3 n
-21
remember, n = 1    2    3  4  5  6
sequence
zero'th term = -2   3    8    15 24 35 48
1st difference =       5    7   9 11 13 15
2nd difference =         2    2  2  2  2

Half the
second
difference \/                        \/ the zero'th term
so, nth term =        1 n^2+      a n+         -2
/\ work out by substituting n
into this equation and rearranging

a sequence or nth term is quadratic when the 1st difference go
by the same amount every time, such that the 2nd difference is
7

63

ero'th term

uting n
rearranging

difference goes up or down
d difference is equal

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