Question

Use the explicit formula an = a1 + (n - 1) • d to find the 500th term of the sequence below.

24, 30, 36, 42, 48, ...

Answer 1

a=24
d=6
n=500

an=24+(500-1)6
an=24+(499x6)
an=24+2994
an=3018

Answer 2

The given sequence is: 24, 30, 36, 42, 48, ...500th of this sequence is 3018.

What is arithmetic sequence?

An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.

If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:

a, a + d, a +  2d, ... , a + (n+1)d, ...

Its nth term is

$T_n = a + (n-1)d$

(for all positive integer values of n)

Where , an = nth term.

a1 = First term

and d = common difference.

The given sequence is: 24, 30, 36, 42, 48, ...

Here = 24,

d = 30-24 = 6

We need to find the 500th term,

So, n = 500.

Now step is to plug in these values in the above formula.

Therefore,

$a_n=24+(500-1)6\\a_n=24+(499 \times 6)\\a_n=24+2994\\a_n=3018$

Therefore, 500th of this sequence is 3018.

Learn more about arithmetic sequence here:

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