Student Question

Find the first term and the common difference of the arithmetic sequence if a2-a6+a4=-7 and a8-a7=2a4

Expert Answers

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The nth term of an arithmetic sequence can be written as a + (n - 1)*d, where a is the first term and d is the common difference.

We have a2-a6+a4=-7

=> a + d - a - 5d + a + 3d = -7

=> a - d = -7

=> d = a + 7

a8 - a7 = 2*a4

=> a + 7d - a - 6d = 2*(a + 3d)

=> d = 2a + 6d

=> 2a + 5d = 0

Now substitute d = a + 7 in  2a + 5d = 0

=> 2a + 5(a + 7) = 0

=> 2a + 5a + 35 = 0

=> 7a + 35 = 0

=> a = -35/7

=> a = -5

d = a + 7 = -5 + 7 = 2

The first term is -5 and the common difference is 2

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