Question

21. Find the nth term for the sequence 1, 5, 9, 13, ...

22. Explain why 95 will not be a term in the sequence given in Q21.

Answer 1

21.
an=a1+d(n-1)
a1=first term
an=nth term
d=common differnce
n=which term

firs term is 1
common differnce is 4 (1+4=5)
so

an=1+4(n-1)
or
an=1+4n-4
an=-3+4n


22.

solve for n such that
-3+4n=95
add 3 to both sides
4n=98
divide both sides by 4
n=24.5
we can't have a non-whole number for n because it names a number, we can't have the 24.5th number, we can have the 24th or 25th, but not the 24.5th