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Question 1119562: Hi, could you help me with this question here please?
"Write the explicit rule for this arithmetic sequence. The 4th term = 5, and the 10th term = 23"
Thank you!
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the formula for an arithmetic sequence is:
An = A1 + (n-1) * d
your 4th term is equal to 5 and your 10th term is equal to 23.
using the formula, you get:
A4 = A1 + (4-1) * d
A10 = A1 + (9-1) * d
these simplify to:
A4 = A1 + 3d
A10 = A1 + 9d
you are given that A4 = 5 and A10 = 23.
the formulas become:
5 = A1 + 3d
23 = A1 + 9d
subtract the first formula from the second to get:
18 = 6d
solve for d to get d = 3.
in both equations, replace d with 3 to get:
5 = A1 + 3 * 3
23 = A1 + 9 * 3
these simplify to:
5 = A1 + 9
23 = A1 + 27
solve for A1 in both equations to get:
A1 = -4 in the first equation.
A1 = -4 in the second equation.
that's good, since A1 needed to be the same in both equations.
since A1 = -4 and d = 3, your sequence is as follows:
term number term value
1 -4
2 -1
3 2
4 5 ***** 4th term in sequence.
5 8
6 11
7 14
8 17
9 20
10 23 ***** 10th term in sequence.
here's a reference on arithmetic sequences.
https://www.mathsisfun.com/algebra/sequences-sums-arithmetic.html
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