The 20th term of an arithmetic sequence is 27 and the first term is -11. What is the common difference??
using the standard notation:
term(20) = a + 19d = 27
and
a = -11
-11 + 19d = 27
19d = 38
d = 2
the common difference is 2
check:
term(2) = a+19d
=-11 + 19(2)
= -11+38
= 27
To find the common difference in an arithmetic sequence, you can use the formula:
nth term = first term + (n - 1) * common difference
In this case, you are given the 20th term (27) and the first term (-11). Let's plug these values into the formula and solve for the common difference.
27 = -11 + (20 - 1) * common difference
Simplifying the equation:
27 = -11 + 19 * common difference
Now, let's isolate the common difference:
19 * common difference = 27 + 11
19 * common difference = 38
Divide both sides of the equation by 19 to solve for the common difference:
common difference = 38 / 19
common difference = 2
Therefore, the common difference in this arithmetic sequence is 2.