#1**+2 **

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

(4^{2} + 4)/2 * 1.25 = 12.5

12.5 + 2 = 14.5

Answer is g

helperid1839321
Oct 24, 2017

#2**+1 **

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**

Guest Oct 24, 2017

edited by
Guest
Oct 24, 2017