The sum of the given sequence is -6384.
Explanation:
The given Arithmetic sequence is 14 + 8 + 2+ ... + ( 274) + (-280).
- The first term of the sequence = 14
- The last term of the sequence = -280
- The common difference ⇒ 14 - 8 = 6
To find the number of terms in the sequence :
The formula used is

where,
- n is the number of terms.
is the late term which is -280.
is the first term which is 14.- d is the common difference which is 6.
Therefore,

⇒

⇒

⇒

⇒ n = 48, since n cannot be negative.
∴ The number of terms, n = 48.
To find the sum of the arithmetic progression :
The formula used is

where,
- S is the sum of the sequence.
is the first term which is 14.
is the late term which is -280.
Therefore,

⇒

⇒

⇒

∴ The sum of the given sequence is -6384.