Question 612087: write the rule for thr nth term of the arithmetic sequence.
1) 5,,14,23,32,41
2)d=-3;a6=30
3)-1,-4,-7,-10,-13... 4) d=5;a5=40
Answer by Edwin McCravy(20054)   (Show Source):
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The formula to learn for the nth term of arithmetic
sequences is:
an = a1 + (n-1)·d
We determine d by subtracting any term from the next term:
5,14,23,32,41,.....
a2 - a1 = 14 - 5 = 9
a3 - a2 = 23 - 14 = 9
a4 - a3 = 32 - 23 = 9
a5 - a4 = 41 - 32 = 9
So d = 9
an = a1 + (n-1)·d
an = 5 + (n-1)·9
an = 5 + 9(n-1)
an = 5 + 9n - 9
an = 9n - 4
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d=-3;a6=30
an = a1 + (n-1)·d
Substitute n=6
a6 = a1 + (6-1)·(-3)
30 = a1 + (5)(-3)
30 = a1 - 15
45 = a1
an = a1 + (n-1)·(-3)
an = 45 + (-3)(n-1)
an = 45 - 3(n-1)
an = 45 - 3n + 3
an = 48 - 3n
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-1,-4,-7,-10,-13,....
a2 - a1 = -4 - (-1) = -4 + 1 = -3
a3 - a2 = -7 - (-4) = -7 + 4 = -3
a4 - a3 = -10 - (-7) = -10 + 7 = -3
a5 - a4 = -13 - (-10) = -13 + 10 = -3
So d = -3
an = a1 + (n-1)·d
an = -1 + (n-1)·(-3)
an = -1 + (-3)(n-1)
an = -1 - 3(n-1)
an = -1 - 3n + 3
an = 2 - 3n
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d=5;a5=40
an = a1 + (n-1)·d
Substitute n=5
a5 = a1 + (5-1)·(5)
40 = a1 + (4)(5)
40 = a1 + 20
20 = a1
an = a1 + (n-1)·(5)
an = 20 + 5(n-1)
an = 20 + 5n - 5
an = 15 + 5n
Edwin
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