The sum of the given sequence is -24846.
<u>Step-by-step explanation:</u>
The given Arithmetic sequence is 46 + 42 +38... +(-446) +(-450).
- The first term of the sequence = 46
- The last term of the sequence = -450
- The common difference ⇒ 46 - 42 = 4
<u>To find the number of terms in the sequence :</u>
The formula used is
where,
- n is the number of terms.
is the late term which is -450.
is the first term which is 46.
- d is the common difference which is 4.
Therefore,
⇒
⇒
⇒
⇒ n = 123, since n cannot be negative.
∴ The number of terms, n = 123.
<u>To find the sum of the arithmetic progression :</u>
The formula used is
where,
- S is the sum of the sequence.
Therefore,
⇒
⇒
⇒
∴ The sum of the given sequence is -24846.