Question

A rule for nth term of -2 , -5/4 ,-1/2,1/4

Answer 1

Answer:

Step-by-step explanation:

This is an arithmetic sequence

a1 = -2

Difference = 2nd term - first term

$=\frac{-5}{4}-[-2]\\\\=\frac{-5}{4}+2\\\\=\frac{-5}{4}+\frac{2*4}{1*4}\\\\=\frac{-5+8}{4}=\frac{3}{4}$

$a_{n}=a+(n-1)d\\\\=-2+(n-1)*(\frac{3}{4})\\\\=-2+\frac{3}{4}n-\frac{3}{4}\\\\=\frac{-2*4}{1*4}-\frac{3}{4}+\frac{3}{4}n\\\\=\frac{-8-3}{4}+\frac{3}{4}n\\\\=\frac{-11}{4}+\frac{3}{4}n$