Question

If the second term of an arithmetic progression is negative 3 and the fourth term is 7​, find the eighth term.

Answer 1

Answer:

  27

Step-by-step explanation:

The 2nd and 4th terms differ by 7-(-3) = 10. The difference between any terms that are 2 apart will be 10, so the 6th and 8th terms are ...

  7 +10 = 17 . . . 6th term

  17 +10 = 27 . . . 8th term

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A more conventional solution might have you find the equation for a general term. You would start with the form of that, then solve for the parameters of it.

  an = a1 +d(n -1)

  a2 = a1 +d(2 -1) = -3

  a4 = a1 + d(4 -1) = 7

Subtracting the equation for a2 from that for a4, we get ...

  a4 -a2 = (a1 +3d) -(a1 +d) = (7) -(-3)

  2d = 10 . . . . . .  simplify

  d = 5 . . . . . . . .  divide by 2 (common difference)

  -3 = a1 +5 . . . . . substitute into equation for a2

  -8 = a1 . . . . . . . .(first term of the sequence)

Now we know the general term can be found from ...

  an = -8 +5(n -1)

Then the 8th term is ...

  a8 = -8 +5(8 -1) = -8 +35 = 27 . . . . same as above

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Alternate approach

After you've done a few of these, you realize that the difference between terms 2 apart is twice the common difference. So, the common difference is ...

  (7 -(-3))/2 = 5 . . . . as we found in the last section

You know the 4th term, so the general term can also be written as ...

  an = a4 +d(n -4) . . . . . . note use of a4 and -4, instead of a1 and -1 above

  an = 7 +5(n -4)

Now, the 8th term is computed as ...

  a8 = 7 + 5(8-4) = 7 +20 = 27