Exercise 72 Page 290

Let's begin by writing the explicit formula for an arithmetic sequence.

a_{n} = a_{1} + (n - 1) d

In this form,

a_{1}

is the first term in the sequence,

d

n

is the position of the desired term in the sequence. Let's observe the given terms in the sequence to determine the value of

d .

0.5 \to + 0.5 1 \to + 0.5 1.5 \to + 0.5 2

Using the common difference

d = 0.5

and the first term

a_{1} = 0.5

, we can write and simplify the equation for the

n th

term of the sequence.

a_{n} = a_{1} + (n - 1) d

$a_{1} = 0.5$ , $d = 0.5$

a_{n} = 0.5 + (n - 1) (0.5)

Distribute $0.5$

a_{n} = 0.5 + 0.5 n - 0.5

Subtract term

a_{n} = 0.5 n

To find the value of the

50 th

term, we substitute

n = 50

into this equation and solve for

a_{50} .

a_{n} = 0.5 n

$n = 50$

a_{50} = 0.5 (50)

a_{50} = 25

The

50 th

term in the sequence is

25 .