Answer and step-by-step explanation:
To find the sum of the first 60 positive even integers, make the sequence first.
2, 4, 6, 8, 10, ... a60
4 - 2 = 2
6 - 4 = 2
8 - 6 = 2
10 - 8 = 2
The sequence is a finite arithmetic sequence because it has a common difference of 2.
Then find the 60th term of the sequence. This will be used to find the sum of the 60 terms.
The formula for an arithmetic sequence is:
An = A1 + (n - 1)d
where
An is the nth term,
A1 is the first term,
n is the number of terms and
d is the common difference.
Substitute the given values to the formula. Then simplify.
An = A60
A1 = 2
n = 60
d = 2
A60 = 2 + (60 - 1)2
A60 = 2 + (59)2
A60 = 2 + 118
A60 = 120
Then use the formula for an arithmetic series which is
Sn = n(A1 + An) /2
Substitute and simplify.
S60 = 60(2 + 120) /2
S60 = 60(122) /2
S60 = 7320/2
S60 = 3660
