Question

the sum of the first ten terms of a linear sequence is -60 and the sum of the first fifteen terms is -165. Find the 18th term of the sequence​

Answer 1

a₁₈ = - 31

Explanation:

`S_(10)=(2a_1+d(10-1))/(2)\cdot 10\\\\(2a_1+9d)/(2)\cdot 10=-60\\\\(2a_1+9d)/(2)=-6\\\\2a_1+9d=-12\\\\2a_1=-12-9d\\\\\\S_(15)=(2a_1+d(15-1))/(2)\cdot 15\\\\(2a_1+14d)/(2)\cdot 15=-165\\\\(2a_1+14d)/(2)=-11\\\\2a_1+14d=-22\\\\-12-9d+14d=-22\\\\ 5d=-10 \\\\ d=-2\\\\\\2a_1=-12-9(-2)=-12+18=6\\\\a_1=3\\\\\\ a_(18)=a_1+17d=3+17(-2)=3-34=-31`