Question

Please help ASAP!!

What is the explicit formula for the arithmetic sequence 4/5 29/30 17/15 13/10

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=(4)/(5) \\\\d=(29)/(30) -(4)/(5) = (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=(4)/(5) +(n-1) (1)/(6)`

On distributing 1/6 over the parenthesis, we get

`(n)/(6)-(1)/(6)+(4)/(5)`

`a_n=(n)/(6) +(19)/(30)`

`a_n=(5n+19)/(30)`

Therefore, the explicit formula is given by

`a_n=f(n)=(5n+19)/(30)`