Arithmetic Sequence? Find the first five terms of the sequence,

texelaare

texelaare

Answered question

2021-08-15

Arithmetic Sequence? Find the first five terms of the sequence, and determine whether it is arithmetic. If it is arithmetic, find the common difference, and express the nth term of the sequence in the standard form an=a+(n1)d
an=4+2n

Answer & Explanation

liannemdh

liannemdh

Skilled2021-08-16Added 106 answers

To find:
The first five terms of the sequence, and check whether it is arithmetic sequence or not. If it is arithmetic sequence, find the common difference, and express the nth term of the sequence in the standard form an=a+(n1)d
Concept used:
The difference between the successive terms of an arithmetic sequence is constant.
Calculation:
Given sequence is,
an=4+2n .......(1)
Substitute 1 for n in equation (1) to calculate the first term of this sequence.
a1=4+21
=4+2
=6
Substitute 2 for n in equation (1) to calculate the second term of this sequence.
a2=4+22
=4+4
=8
Substitute 3 for n equation (1) to calculate the third term of this sequence.
a3=4+23
=4+8
=12
Substitute 4 for n equation (1) to calculate the fourth term of this sequence.
a4=4+24
=4+16
=20
Substitute 5 for n equation (1) to calculate the fifth term of this sequence.
a5=4+25
=4+32
=36
Difference between first and second term can be calculated as,
a2a1=86
=2
Difference between second and third term can be calculated as,
a3a2=128
=4
Since, the difference between the successive terms of the given sequence is not constant.
Therefore, the sequence an=4+2n is not arithmetic.
Conclusion:
Hence, the sequence an=4+2n is not arithmetic.
Jeffrey Jordon

Jeffrey Jordon

Expert2022-07-07Added 2605 answers

Answer is given below (on video)

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?