Question 1119562
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:


<pre>

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.

</pre>


here's a reference on arithmetic sequences.


<a href = "https://www.mathsisfun.com/algebra/sequences-sums-arithmetic.html" target = "" target = "_blank">https://www.mathsisfun.com/algebra/sequences-sums-arithmetic.html</a>