# If the 7th term of a sequence is 33 and the 10th term is 21, find the common difference d?

Dec 7, 2016

$d = - 4$

#### Explanation:

Given conditions are
$a 7 = 33$
$a 10 = 21$
we have to find 'd'
we have arithmetic sequence relation
$a n = a + \left(n - 1\right) d$
from given data we can write
$a 7 = a + \left(7 - 1\right) d$
$33 = a + 6 d$........ (1)
and
$a 10 = a + \left(10 - 1\right) d$
$21 = a + 9 d$........(2)
Subtract eq (2) from (1) we have now
$- 12 = 3 d$
Therefore
$d = - 4$