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adell [148]
3 years ago
6

For the following​ sequence, determine if it is an arithmetic​sequence, a geometric​ sequence, or neither. If it is either arith

metic or​ geometric, give the next term in the sequence.
5​, 8​,13​, 21​, 34​, 55,...
Mathematics
1 answer:
Bumek [7]3 years ago
4 0

Answer:

Neither

Step-by-step explanation:

We are given that a sequence

5,8,13,21,34,55,....

We have to determine the sequence is an arithmetic , geometric or neither.

a_1=5,a_2=8,a_3=13,...a_6=55

We know that if a sequence is an arithmetic then the difference between consecutive terms are equal.

If a sequence is geometric then the ratio of consecutive terms is constant.

d_1=a_2-a_1=8-5=3

d_2=a_3-a_2=13-8=5

d_1\neq d_2

Hence, the difference between the consecutive terms is not equal .Therefore, sequence is not an arithmetic sequence.

r_1=\frac{a_2}{a_1}=\frac{8}{5}

r_2=\frac{a_3}{a_2}=\frac{13}{8}

r_1\neq r_2

Hence, the ratio of consecutive terms is not equal .Therefore, given sequence is not geometric sequence.

Therefore, given sequence is not an arithmetic nor geometric sequence.

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If angle ABC is one degree less than three times angle ABD and angle DBC=47 find each measure
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It has not been indicated whether the figure in the questions is a triangle or a quadrilateral. Irrespective of the shape, this can be solved. The two possible shapes and angles have been indicated in the attached image.

Now, from the information given we can infer that there is a line BD that cuts angle ABC in two parts: angle ABD and angle DBC

⇒ Angle ABC = Angle ABD + Angle DBC

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Substituting the values in the above equations

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⇒ x = 24

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