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

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

Dec 14, 2018

#1
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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

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