Question

If the common difference between the terms of the sequence is -15, what term follows the term that has the value 15?

Answer 1

The term following 15, for an arithmetic progression with a common difference of -15 would be 0.

Briefly, an arithmetic progression is a series of numbers which start with a base value and progresses with each succeeding term, differing from the preceding term by a common difference.

A generic series will be:
`a, a+d, a+2d,..... a+(n-1)d`
where

• `a` is the 1st term
• `d` is the common difference
• `a+(n-1)*d` is the `n^(th)` term of the sequence

Now, if `p` (assume) be some `r^(th)` term of the sequence, the `(r+1)^(th)` term would be `p+d`

So, for a series with 15 as 1st term and common difference -15, the 2nd term would be,

`15+(2-1)*-15 = 0`

If 15 is any term along the series and not necessarily the 1st term, then the next term would again be,

`15+(-15) = 0`