Question

Please help ASAP!!

Answer 1

The answer is D, 
a(n) = 4/5 + 1/6(n- 1)
just took the test :)

Answer 2

We have been given the arithmetic sequence 4/5 , 29/30,  17/15 , 13/10

Let a be the first term and d be the common difference of the arithmetic sequence.

So let us first find the a and d

$a=\frac{4}{5} \\\\d=\frac{29}{30} -\frac{4}{5} = \frac{1}{6}$

We know the nth term of an arithmetic sequence is given by

$a_n=a+(n-1)d$

On substituting the known values, we get

$a_n=\frac{4}{5} +(n-1) \frac{1}{6}$

On distributing 1/6 over the parenthesis, we get

$\frac{n}{6}-\frac{1}{6}+\frac{4}{5}$

$a_n=\frac{n}{6} +\frac{19}{30}$

$a_n=\frac{5n+19}{30}$

Therefore, the explicit formula is given by

$a_n=f(n)=\frac{5n+19}{30}$