The fith term of the arithmetic sequence is 23 and the 12th term is 72 what is the value of the 10th
term in the arithmetic sequence?
Let's denoted the first term of the arithmetic sequence as "a" and the common difference as "d".
Using the formula for the nth term of an arithmetic sequence, we can set up two equations based on the given information:
a + 4d = 23 (since the fifth term is 23)
a + 11d = 72 (since the twelfth term is 72)
Now, we can solve these equations to find the values of "a" and "d".
Subtracting the first equation from the second equation, we get:
(72) - (23) = (a + 11d) - (a + 4d)
49 = 7d
d = 7
Substituting the value of "d" back into the first equation, we get:
a + 4(7) = 23
a + 28 = 23
a = -5
Now, we have found the values of "a" and "d". We can use the formula for the nth term of an arithmetic sequence to find the value of the 10th term.
10th term = a + (10 - 1)d
10th term = -5 + (10 - 1)(7)
10th term = -5 + 9(7)
10th term = -5 + 63
10th term = 58
Therefore, the value of the 10th term in the arithmetic sequence is 58.