Sequences and Series 1.[4.K] Is each sequence arithmetic, geometri

philosphy111of

philosphy111of

Answered question

2021-11-16

Sequences and Series
1.[4.K] Is each sequence arithmetic, geometric or neither? State the general term (simplify fully).
a)81,75,69,...
b)2187,729,243,...
2.[2,K] Determine the first four terms of the sequence if the general term is tn=5n+22n+1.

Answer & Explanation

Jeffrey Parrish

Jeffrey Parrish

Beginner2021-11-17Added 15 answers

Step 1
Q.1 (a) Given sequence 81, 75, 69,.....
Aseries or sequence in which common difference of two consecutive terms are equal is called an arithmetic series or sequence.
Common Difference,7581=6975=6
Since, the common difference between two consecutive terms of the given sequence is same, therefore, this sequence is an Arithmetic Progession.
The general term of an arithmetic sequence is written in terms of its first term a_{1}, common difference d and index n as follows, an=a1+(n1)d
Step2
Q.1 (b) Given sequence 2187, 729, 243,......
A series or sequence in which common ratio of two consecutive terms are equal is called an arithmetic series or sequence.
Common Ratio,7292187=243729=0.33
Since, the common ratio between two consecutive terms of the given sequence is same, therefore, this sequence is a Geometric Progession.
The general term of a geometric sequence is written in terms of its first term a1, common ratio r and index n as follows,an=arn1
Step3
Q.2Given,tn=5n+22n+1
First four terms of the sequence can be determined by putting the value of n as 1, 2, 3 and 4, Therefore,
t1=5x1+22x1+1=5+22+1=73
t2=5x2+22x2+1=10+24+1=125
t3=5x3+22x3+1=15+26+1=177
t4=5x4+22x4+1=20+28+1=229.

Jeffrey Jordon

Jeffrey Jordon

Expert2022-08-30Added 2605 answers

Answer is given below (on video)

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