Find the first term and the common difference of the arithmetic sequence whose 7th term is 19 and 20th term is 71.

Guest Dec 14, 2018

#1**+1 **

Solve the following system:

{19 = 6 A + F | (equation 1)

71 = 19 A + F | (equation 2)

Express the system in standard form:

{-F - 6 A = -19 | (equation 1)

-F - 19 A = -71 | (equation 2)

Subtract equation 1 from equation 2:

{-F - 6 A = -19 | (equation 1)

0 F - 13 A = -52 | (equation 2)

Multiply equation 1 by -1:

{F + 6 A = 19 | (equation 1)

0 F - 13 A = -52 | (equation 2)

Divide equation 2 by -13:

{F + 6 A = 19 | (equation 1)

0 F+A = 4 | (equation 2)

Subtract 6 × (equation 2) from equation 1:

{F+0 A = -5 | (equation 1)

0 F+A = 4 | (equation 2)

** F = -5 - First term and A =4 - Common difference**

Guest Dec 14, 2018

#1**+1 **

Best Answer

Solve the following system:

{19 = 6 A + F | (equation 1)

71 = 19 A + F | (equation 2)

Express the system in standard form:

{-F - 6 A = -19 | (equation 1)

-F - 19 A = -71 | (equation 2)

Subtract equation 1 from equation 2:

{-F - 6 A = -19 | (equation 1)

0 F - 13 A = -52 | (equation 2)

Multiply equation 1 by -1:

{F + 6 A = 19 | (equation 1)

0 F - 13 A = -52 | (equation 2)

Divide equation 2 by -13:

{F + 6 A = 19 | (equation 1)

0 F+A = 4 | (equation 2)

Subtract 6 × (equation 2) from equation 1:

{F+0 A = -5 | (equation 1)

0 F+A = 4 | (equation 2)

** F = -5 - First term and A =4 - Common difference**

Guest Dec 14, 2018