peachieweachie
Answered

Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Our platform connects you with professionals ready to provide precise answers to all your questions in various areas of expertise. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

Work out an expression for the nth term for this sequence:

23,35,47,49

Sagot :

Happil

Answer:

[tex]a_n = 23 +12(n -1)[/tex]

Explanation:

The [tex]n[/tex]th term of an arithmetic sequence is explicitly defined as [tex]a_n = a_1 +d(n -1)[/tex] where [tex]a_1[/tex] is the first term of the sequence and [tex]d[/tex] is the the common difference.

From the given first five terms of the sequence we can see that the first term is [tex]23[/tex] so [tex]a_1 = 23[/tex].

The common difference, [tex]d[/tex], can be calculated by [tex]a_n - a_{n -1}[/tex] so we'll find the common difference of the given sequence by letting [tex]n = 2[/tex]

[tex]d = a_2 - a_{2 -1} \\d = a_2 -a_{1} \\d = 35 -23 \\ d = 12[/tex].

Now let's plug everything we know.

[tex]a_1 = 23[/tex]

[tex]d = 12[/tex]

[tex]a_n = 23 + 12(n -1)[/tex]

We hope this was helpful. Please come back whenever you need more information or answers to your queries. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.