HOW TO DO THIS

Arithmetic Sequence: t(n) = m*n + b (Linear)

t(6) = 8

t(10) = 13

t difference = 4

output difference = 5

m = 1.25

6*1.25=7.5

8-7.5 = 0.5

t(n)=1.25n + 0.5

Sequences start at one. I am taking a shortcut on this by using a formula I know to quickly take the sum of any numbers in sequence:

0.5*4 = 2

(4² + 4)/2 * 1.25 = 12.5

12.5 + 2 = 14.5

Answer is g

Solve the following system:  where F = First term,  D=Common difference
{5 D + F = 8 | (equation 1)
9 D + F = 13 | (equation 2)

Subtract equation 1 from equation 2:
{F + 5 D = 8 | (equation 1)
0 F+4 D = 5 | (equation 2)

Divide equation 2 by 4:
{F + 5 D = 8 | (equation 1)
0 F+D = 5/4 | (equation 2)

Subtract 5 × (equation 2) from equation 1:
{F+0 D = 7/4 | (equation 1)
0 F+D = 5/4 | (equation 2)

F = 7/4 First term       and        D = 5/4 Common difference

The Sequence is: 7/4 + 12/4 + 17/4 + 22/4 =58/4 =14.50