Find the eight term of an arithmetic sequence whose fourth term is 19 and whose fifteenth term is 52.(1 point)
To find the eight term of an arithmetic sequence, we first need to find the common difference (d) between the terms.
Given that the fourth term is 19, and the fifteenth term is 52, we can write two equations:
a + 3d = 19 (equation 1)
a + 14d = 52 (equation 2)
where a is the first term of the sequence.
Subtracting equation 1 from equation 2, we get:
11d = 33
d = 3
Now, we can substitute the common difference back into equation 1 to find the first term of the sequence:
a + 3(3) = 19
a + 9 = 19
a = 10
Now, we can find the eighth term by using the formula for any term of an arithmetic sequence:
a_n = a + (n-1)d
where a_n is the nth term of the sequence. Substituting n = 8:
a_8 = 10 + (8-1)3
a_8 = 10 + 7(3)
a_8 = 10 + 21
a_8 = 31
Therefore, the eighth term of the arithmetic sequence is 31.