Find the number of terms of the arithmetic sequence with the given description that must be added to get a value of 3360.The first term is 5, and the common difference is 2.

To solve this problem, we need to use the formula for the sum of an arithmetic series:

S_n = n/2 * (a_1 + a_n)

where: S_n is the sum of the first n terms, n is the number of terms, a_1 is the first term, and a_n is the nth term.

We know that S_n = 3360, a_1 = 5, and the common difference d = 2. We don't know n or a_n, but we can express a_n in terms of n and d:

a_n = a_1 + (n - 1)*d a_n = 5 + (n - 1)*2 a_n = 5 + 2n - 2 a_n = 2n + 3

Substitute a_n and S_n into the sum formula:

3360 = n/2 * (5 + 2n + 3) 3360 = n/2 * (8 + 2n) 3360 = n/2 * 2n + 8 3360 = n^2 + 4n

Rearrange to form a quadratic equation:

n^2 + 4n - 3360 = 0

Solve this quadratic equation for n. The solutions are n = 60 and n = -56. Since n can't be negative, the number of terms that must be added to get a value of 3360 is 60.