Question

Find the rule for the sequence First term: 2 3/4 Sixth term: 3 7/12 Rule:_______

Answer 1

K, so areitmetic

an=a1+d(n-1)
a1=first term
d=common differnce

we are given
a1=2 and 3/4
6th term is 3 and 7/12

so

a6=3 and 7/12=2 and 3/4+d(6-1)
3 and 7/12=2 and 3/4+d(5)
minus 2 and 3/4 both sides
10/12=5d
divide both sides by 5 or multiply both sides by 1/5
2/12=d
1/6=d


$a_n=2 \frac{3}{4}+ \frac{1}{6}(n-1)$ or
$a_n=2 \frac{7}{12}+ \frac{1}{6}n$
that is the rule