Question

Write an equation for the nth term of the arithmetic sequence. Then find a50.

1/3 , 1/2 , 2/3 , 5/6

Answer 1

Explanation:

Since the sequence above is an arithmetic sequence

For an nth term in an arithmetic sequence

A(n) = a + ( n - 1)d

where a is the first term

n is the number of terms

d is the common difference

From the question

a = 1/3

d = 1/2 - 1/3 = 1/6 or 2/3 - 1/2 = 1/6

Substitute the values into the above formula

That's

`A(n) = (1)/(3) + (n - 1) (1)/(6) \\ = (1)/( 3) - (1)/(6) + (1)/(6) n`

So the nth term of the sequence is

`A(n) = (1)/(6) + (1)/(6)n`

For a50 since we are finding the 50th term

n = 50

So we have

`A(50) = (1)/(6) + (1)/(6) (50) \\ = (1)/(6) + (25)/(3)`

We have the final answer as

`A(50) = (17)/(2)`

Hope this helps you