Subtract the first term from the second term to find the common difference.

$\displaystyle 26-14=12$

Subtract the first term from the second term to find the common difference.

$\displaystyle 8-(-5)=8+5=13$

Subtract the first term from the second term to find the common difference.

$\displaystyle -16-(-21)=-16+21=5$

Subtract the first term from the second term to find the common difference.

$\displaystyle 17-15=2$

Subtract the first term from the second term to find the common difference.

$\displaystyle -2-(-10)=-2+10=8$

Subtract the first term from the second term to find the common difference.

$\displaystyle -\frac{2}{3}-\left(-\frac{8}{3}\right)=-\frac{2}{3}+\frac{8}{3}=\frac{6}{3}=2$

Subtract the first term from the second term to find the common difference.

$\displaystyle -9-(-15)=-9+15=6$

The measures of the five angles of a pentagon add up to $\displaystyle 180^o (5-2) = 540^o$, based on the formula $\displaystyle 180^o(n-2)$.

If the measures of the five angles form an arithmetic sequence, the angles have measures increasing by a some common difference, $\displaystyle d$.

$\displaystyle 70,70+d,70+2d,70+3d,70+4d$ 

Given this pattern and the total sum, we can solve for the common difference.

$\displaystyle 70+ \left( 70+d\right )+\left( 70+2d\right )+\left( 70+3d\right )+\left( 70+4d\right ) = 540$

$\displaystyle 350+10d = 540$

$\displaystyle 10d = 190$

$\displaystyle d=19$

The greatest of the angle measures is given by $\displaystyle 70+4d$.

$\displaystyle 70+4d = 70 + (4 )(19) = 146^{\circ }$

The question is basically asking you to find the sum of the first $\displaystyle 11$ terms of the following arithmetic sequence:

$\displaystyle 4, 6, 8...$

To find the sum of a certain number of terms in an arithmetic sequence, use the following formula:

$\displaystyle \text{Sum}=\frac{n(y_1+y_n)}{2}$

• $\displaystyle n=$ the number of the terms you have
• $\displaystyle y_1=$ the first term of the sequence
• $\displaystyle y_n=n^{th}$ term of the sequence

To find the sum, we need to first find the 11th term of the sequence.

To find any term in an arithmetic sequence, use the following formula:

$\displaystyle y_n=a_1+(n-1)d$

• $\displaystyle y_n$ is the term we want to find
• $\displaystyle a_1$ is the first term of the sequence
• $\displaystyle n$ is the number of the term we want to find
• $\displaystyle d$ is the common difference

Using the information given from the question, 

$\displaystyle a_1=4$

$\displaystyle n=11$

$\displaystyle d=6-4=2$

Now, plug in the information to find the value of the 11th term.

$\displaystyle y_{11}=4+(11-1)(2)=4+(10)(2)=4+20=24$

Now that we know the 11th term of the sequence, we can plug in that value into the equation for the sum to find what these first 11 terms add up to.

$\displaystyle \text{Sum}=\frac{11(4+24)}{2}=\frac{11(28)}{2}=154$

To find any term in an arithmetic sequence, use the following formula:

$\displaystyle y_n=a_1+(n-1)d$

• $\displaystyle y_n$ is the term we want to find
• $\displaystyle a_1$ is the first term of the sequence
• $\displaystyle n$ is the number of the term we want to find
• $\displaystyle d$ is the common difference

For this sequence, 

$\displaystyle a_1=-8$

$\displaystyle n=8$

$\displaystyle d=-2-(-8)=6$

Now, plug in the information to find the value of the 8th term.

$\displaystyle y_8=-8+(8-1)6=-8+(7)6=-8+42=34$