Question

Topic - n-th term

If x + 1 and -x + 17 are the second and sixth terms of a sequence with a common difference
of 5, find the value of x.

Answer 1

Answer: -2

Explanation:

So, the arithmetic sequence formula for the nth term is as follows.

Tₙ = a + (n-1)d

So,

2nd term or (x + 1) = a + d

x + 1 = a + 5 (d = 5). - 1

6th term or (-x + 17) = a + 5d

- x + 17 = a + 25. - 2

Subtract 2 from 1, we get,

2x - 16 = -20

2x = -4

x = -2

You can check it if you want,

Second term = - 1

Sixth term will be - 1 + 5 + 5 + 5 + 5 = 19

There you go.