Which expression defines the given series for seven terms?
8 + 13 + 18 + . . .
The common difference between each term in the series is 5. To find the expression that defines the given series for seven terms, we can use the formula for the nth term of an arithmetic sequence:
a_n = a_1 + (n - 1)d
where a_n is the nth term, a_1 is the first term, n is the number of terms, and d is the common difference.
For this series, the first term is 8 and the common difference is 5. Plugging those values into the formula:
a_n = 8 + (n - 1)5
To find the expression for the seventh term (n = 7):
a_7 = 8 + (7 - 1)5
Simplifying:
a_7 = 8 + 6(5)
a_7 = 8 + 30
a_7 = 38
Therefore, the expression that defines the given series for seven terms is 8 + 13 + 18 + ... + 38.