The sum of the given sequence is -6384.
<u>Step-by-step explanation:</u>
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
<u>To find the number of terms in the sequence :</u>
The formula used is ![n = (\frac{a_{n}-a_{1}} {d})+1](https://tex.z-dn.net/?f=n%20%3D%20%28%5Cfrac%7Ba_%7Bn%7D-a_%7B1%7D%7D%20%7Bd%7D%29%2B1)
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 =(\frac{-280-14}{6}) +1](https://tex.z-dn.net/?f=n%20%3D%28%5Cfrac%7B-280-14%7D%7B6%7D%29%20%2B1)
⇒ ![n =( \frac{-294}{6}) + 1](https://tex.z-dn.net/?f=n%20%3D%28%20%5Cfrac%7B-294%7D%7B6%7D%29%20%2B%201)
⇒ ![n = -49 + 1](https://tex.z-dn.net/?f=n%20%3D%20-49%20%2B%201)
⇒ ![n = -48](https://tex.z-dn.net/?f=n%20%3D%20-48)
⇒ n = 48, since n cannot be negative.
∴ The number of terms, n = 48.
<u>To find the sum of the arithmetic progression :</u>
The formula used is ![S = \frac{n}{2}(a_{1} + a_{n} )](https://tex.z-dn.net/?f=S%20%3D%20%5Cfrac%7Bn%7D%7B2%7D%28a_%7B1%7D%20%2B%20a_%7Bn%7D%20%29)
where,
- S is the sum of the sequence.
is the first term which is 14.
is the late term which is -280.
Therefore, ![S = \frac{48}{2}(14+ (-280))](https://tex.z-dn.net/?f=S%20%3D%20%5Cfrac%7B48%7D%7B2%7D%2814%2B%20%28-280%29%29)
⇒ ![S = \frac{48}{2}(-266)](https://tex.z-dn.net/?f=S%20%3D%20%5Cfrac%7B48%7D%7B2%7D%28-266%29)
⇒ ![S = 48 \times -133](https://tex.z-dn.net/?f=S%20%3D%2048%20%5Ctimes%20-133)
⇒ ![S = -6384](https://tex.z-dn.net/?f=S%20%3D%20-6384)
∴ The sum of the given sequence is -6384.
The answer is 5501.83784
I am not going to say much, but that is the answer i got, hope it helps
Answer:
The number 5 multiplied by -1 then by 2 then by -3 then by 4....... (alternating positive and negative
Step-by-step explanation:
5*-1 = -5
5*2 = 10
5*-3= -15
5*4= 20
5*-5 = -25 ......
Answer:
this the answer 4.5m
Step-by-step explanation:
formula 1/2(a+b)h