Question

Find the 8th term of the arithmetic sequence -2x+5−2x+5, -7x+8−7x+8, -12x+11, ...

Answer 1

Answer:

  -37x+26

Step-by-step explanation:

The x-coefficients have the sequence ...

  -2, -7, -12, ...

which has first term -2 and common difference of (-7 -(-2)) = -5. Then the 8th x-coefficient is ...

  -2 + (-5)(8 -1) = -37

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The constants have the sequence ...

  5, 8, 11, ...

which has first term 5 and common difference 8 -5 = 3. Then the 8th constant term is ...

  5 +(3)(8 -1) = 26

The 8th term of the sequence is -37x +26.

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The general term of an arithmetic sequence with first term a1 and common difference d is ...

  an = a1 +d(n -1)

In the above, we have used n=8 to find the 8th term.