The given sequence is expressed as
4 + 11 + 18 + …+ 88
We can see that there is a common difference, d between consecutive terms.
d = 11 - 4 = 18 - 11
d = 7
The series is an arithmetic series because there is a common difference between consecutive terms. We would find the number of terms in the series by applying the formula for determining the nth term of an arithmetic sequence which is expressed as
an = a1 + (n - 1)d
a1 is the first term = 4
d = common difference = 7
For the last term, we have
88 = 4 + (n - 1)7
88 = 4 + 7n - 7
88 - 4 + 7 = 7n
91 = 7n
n = 91/7
n = 13
There are 13 terms in the series
We would find the sum of the series by applying the formula
Sn = n/2(a + l)
where
l is the last term
a is the first term
From the information given,
l = 88
a = 4
n = 13
Sn = 13/2(4 + 88)
Sn = 598
The sum of the terms in the sequence is 598