Given an arithmetic sequence with a7 4 and a19 14 find a30So

Given an arithmetic sequence with a_7 =4 and a_19 -14, find a_30

Solution

nth term of arithmetic series is given by

a_n=a₁+(n-1)d

a₇=a₁+ 6d= 4

a₁₉=a₁+18d= -14

From these two equations we get

-12d= 18

d=-1.5

4=a₁+6(-1.5)

a₁= 13

a₃₀=13 + 29(-1.5)= -30.5