Step 1. Find the Greatest Common Factor (GCF)
GCF = 7x^2
Step 2. Factor out the GCF (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
7x^2(14x^4/7x^2 + 35x^2/7x^2)
Step 3. Simplify each term in parentheses
7x^2(2x^2 + 5)
Hi,
The sum of the measures of the interior angles of a polygon with x sides is equal to (x-2) times 180 degrees. A pentagon has got 5 sides, so the sum of the measures of its interior angles is 180(5-2) = 180(3) = 540 degrees.
I hope this helps. If I was not clear enough or if you’d like further explanation please let me know. Also, English is not my first language, so I’m sorry for any mistakes.
Answer:Answer:
Step-by-step explanation:
Given the sequence -4,-6,-8..., in order to get sigma notation to represent the sum of the first seven terms of the sequence, we need to first calculate the sum of the first seven terms of the sequence as shown;
The sum of an arithmetic series is expressed as ![S_n = \frac{n}{2}[2a+(n-1)d]](https://tex.z-dn.net/?f=S_n%20%3D%20%5Cfrac%7Bn%7D%7B2%7D%5B2a%2B%28n-1%29d%5D)
n is the number of terms
a is the first term of the sequence
d is the common difference
Given parameters
n = 7, a = -4 and d = -6-(-4) = -8-(-6) = -2
Required
Sum of the first seven terms of the sequence
![S_7 = \frac{7}{2}[2(-4)+(7-1)(-2)]\\\\S_7 = \frac{7}{2}[-8+(6)(-2)]\\\\S_7 = \frac{7}{2}[-8-12]\\\\\\S_7 = \frac{7}{2} * -20\\\\S_7 = -70](https://tex.z-dn.net/?f=S_7%20%3D%20%5Cfrac%7B7%7D%7B2%7D%5B2%28-4%29%2B%287-1%29%28-2%29%5D%5C%5C%5C%5CS_7%20%3D%20%20%5Cfrac%7B7%7D%7B2%7D%5B-8%2B%286%29%28-2%29%5D%5C%5C%5C%5CS_7%20%3D%20%20%5Cfrac%7B7%7D%7B2%7D%5B-8-12%5D%5C%5C%5C%5C%5C%5CS_7%20%3D%20%5Cfrac%7B7%7D%7B2%7D%20%2A%20-20%5C%5C%5C%5CS_7%20%3D%20-70)
The sum of the nth term of the sequence will be;
![S_n = \frac{n}{2}[2(-4)+(n-1)(-2)]\\\\S_n = \frac{n}{2}[-8+(-2n+2)]\\\\S_n = \frac{n}{2}[-6-2n]\\\\S_n = \frac{-6n}{2} - \frac{2n^2}{2}\\S_n = -3n-n^2\\\\S_n = -n(3+n)](https://tex.z-dn.net/?f=S_n%20%3D%20%5Cfrac%7Bn%7D%7B2%7D%5B2%28-4%29%2B%28n-1%29%28-2%29%5D%5C%5C%5C%5CS_n%20%3D%20%5Cfrac%7Bn%7D%7B2%7D%5B-8%2B%28-2n%2B2%29%5D%5C%5C%5C%5CS_n%20%3D%20%5Cfrac%7Bn%7D%7B2%7D%5B-6-2n%5D%5C%5C%5C%5CS_n%20%3D%20%20%5Cfrac%7B-6n%7D%7B2%7D%20-%20%20%5Cfrac%7B2n%5E2%7D%7B2%7D%5C%5CS_n%20%3D%20-3n-n%5E2%5C%5C%5C%5CS_n%20%3D%20-n%283%2Bn%29)
The sigma notation will be expressed as . <em>The limit ranges from 1 to 7 since we are to find the sum of the first seven terms of the series.</em>
36 there you go I hope you understand
