Question

Here are the first 5 terms of an arithmetic sequence. 8, 12, 16, 20 Find an expression, in terms of n, for the nth term of the sequence

Answer 1

Answer:

24

Step-by-step explanation:

8+4=12 12+4=16 16+4=20

20+4=24

Answer 2

The  $n^{th}$ term of an arithmetic sequence is 4+4n.

Given:

An arithmetic sequence 8, 12, 16, and 20.

To Find:

The $n^{th}$ term of the sequence.

Solution:

The given terms of a sequence are said to be in arithmetic progression if the difference between every two consecutive terms is constant.

The  $n^{th}$ term of an arithmetic sequence is denoted by $a_{n}$ = a+(n-1)d.

The given arithmetic sequence is 8, 12, 16, and 20.

The difference between every two consecutive difference is 4.

So, we can write:

The first term, a = 8.

The common difference, d = 4.

Now,

The  $n^{th}$ term of an arithmetic sequence, $a_{n}$ = a+(n-1)d

⇒ $a_{n}$ = 8+(n-1)4 = 8+4n-4 = 4+4n.

Hence, the  $n^{th}$ term of an arithmetic sequence is 4+4n.

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