Question

What is the 52nd term for the following sequence ? 14,6,-2,-10,-18

Answer 1

It's an arithmetic sequence:

`a_1=14\\a_2=14-8=6\\a_3=6-8=-2\\a_4=-2-8=-10\\a_5=-10-8=-18\\\vdots\\\text{The general formula for nth term of an arithmetic sequence}\\\\a_n=a_1+(n-1)d\\\\\text{We have}\ a_1=14,\ d=-8.\\\\\text{Substitute:}\\\\a_n=14+(n-1)(-8)=14-8n+8=22-8n\\\\\text{We need}\ a_(52).\ \text{Put n = 52 to the formula}:\\\\a_(52)=22-8(52)=22-416=-394`