Question 1150834
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Let a = first term
Let d = common difference<br>
10th term: a+9d
15th term: a+14d
18th term: a+17d<br>
Sum of first ten terms: -60 = 10 times average of first and tenth terms<br>
{{{10((a+(a+9d))/2)= -60}}}
{{{2a+9d = -12}}} [1]<br>
Sum of first 15 terms: -165 = 15 times average of first and 15th terms<br.
{{{15((a+(a+14d))/2) = -165}}}
{{{2a+14d = -22}}} [2]<br>
Subtract [1] from [2] and solve for d; then use that value in either [1] or [2] to solve for a.<br>
Finally, use the values of a and d to find the 18th term.<br>