Question

Find a formula for the nth term in this arithmetic sequence: a1=0, a2=0.5, a3=1, a4=1.5...

Answer 1

A formula for the nth term in given arithmetic sequence = 0.5(n - 1) or, $\dfrac{1}{2}$(n - 1)

Step-by-step explanation:

Given,

$a_1$ = 0, $a_2$ = 0.5, $a_3$ = 1, $a_4$ = 1.5, ...

To find, a formula for the nth term in given arithmetic sequence = ?

Here, first term (a) = $a_1$ = 0 and

common difference(d) = $a_2$ - $a_1$ = $a_3$ - $a_2$ = 0.5 - 0 = 0.5

We know that,

The nth term of the arithmetic sequence

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

Put a = 0 and d = 0.5, we get

$a_{n}$ = 0 +(n - 1)0.5

= 0.5(n - 1) or, $\dfrac{1}{2}$(n - 1)

∴ A formula for the nth term in given arithmetic sequence = 0.5(n - 1) or, $\dfrac{1}{2}$(n - 1)