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

Jun 5, 2015

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:
$a , a + d , a + 2 d , \ldots . . a + \left(n - 1\right) d$
where

• $a$ is the 1st term
• $d$ is the common difference
• $a + \left(n - 1\right) \cdot d$ is the ${n}^{t h}$ term of the sequence

Now, if $p$ (assume) be some ${r}^{t h}$ term of the sequence, the ${\left(r + 1\right)}^{t h}$ term would be $p + d$

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

$15 + \left(2 - 1\right) \cdot - 15 = 0$

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

$15 + \left(- 15\right) = 0$