Question

Determine whether the sequence could be arithmetic. If so, find the common difference and the next term.

Answer 1

Take the difference between consecutive terms and see if it is the same throughout the sequence.

Answer 2

\[\frac{ 11 }{ 2 },\frac{ 11 }{ 3 },\frac{ 11 }{ 4 },\frac{ 11 }{ 5 },\frac{ 11 }{ 6 }\]

Answer 3

@Mertsj

Answer 4

@Mertsj

Answer 5

I'll use alternate terms: 11/2-11/4=11/4. If this were an arithmetic sequence, the 5th term would be 11/4-11/4=0. It is not, therefore this is not an arithmetic sequence.

Answer 6

@Luis_Rivera

Answer 7

@Luis_Rivera can you help?

Answer 8

It isn't. It's a geometric relationship, but not a geometric sequence. If it were a geometric sequence, instead of the 1/(n+1) you would have a simple exponential of the ratio r.

Answer 9

so its not arithmetic?

Answer 10

uhh, yes it is geometic

Answer 11

It is neither arithmetic nor geometric...

Answer 12

ok
thx

Answer 13

Arithmetic sequences can be written in the format:\[a_n=a_0+n \times c\]Geometric sequences can be written in the format:\[a_n=a_0 \times r^n\]This sequence is neither.

Answer 14

For the love of... this sequence has a formula:\[a_n=a_0 \div (n+1)\] which is neither of the formulas above, so it's not arithmetic or geometric.

Answer 15

\[uhh, \ \ a _{0} \div{n+1}= a _{0}*\frac{ 1 }{ n+1 }\ \ \ so \ its \ geometric\]

Answer 16

\[a_{n}=a _{1}+(n+1)d\]

Answer 17

@Numb3r1 @Luis_Rivera

Answer 18

thats the real formula

Answer 19

That's not how geometric sequences work, @Luis_Rivera. @tomtom777, your formula is not the neatest formula for an arithmetic sequence, but it works. However, this is NOT AN ARITHMETIC OR GEOMETRIC SEQUENCE. Once more:
Arithmetic sequences can be written in the format:
an=a0+n×c
Geometric sequences can be written in the format:
an=a0×r^n
This sequence is neither:
a0÷(n+1)=a0∗(1÷(n+1)) is NOT ONE OF THE ABOVE FORMULAS. Ignore both of them, they are simply wrong.