Question

Given the sequence -1,3,7,11 find a25

Answer 1

It'a an arithmetic sequence.

`a_1=-1\\a_2=-1+4=3\\a_3=3+4=7\\a_4=7+4=11\\\vdots\\\\\text{The general formula of nth term of an arithmetic sequence:}\\\\a_n=a_1+(n-1)d\\\\\text{We have:}\\\\a_1=-1,\ d=4\\\\\text{Substitute:}\\\\a_n=-1+(n-1)(4)=-1+4n-4=4n-5\\\\\text{We want }\ a_(25).\ \text{Substitute n = 25 to the formula:}\\\\a_(25)=4(25)-5=100-5=95\\\\Answer:\ \boxed{a_(25)=95}`