Question

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

Answer 1

Step-by-step 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

$A(n) = \frac{1}{3} + (n - 1) \frac{1}{6} \\ = \frac{1}{ 3} - \frac{1}{6} + \frac{1}{6} n$

So the nth term of the sequence is

$A(n) = \frac{1}{6} + \frac{1}{6}n$

For a50 since we are finding the 50th term

n = 50

So we have

$A(50) = \frac{1}{6} + \frac{1}{6} (50) \\ = \frac{1}{6} + \frac{25}{3}$

We have the final answer as

$A(50) = \frac{17}{2}$

Hope this helps you