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Domestic bees make their honeycomb by starting with a single hexagonal cell, then forming ring after ring of hexagonal cells around the initial cell, as shown. The number of cells in successive rings forms an arithmetic sequence..
A-Write a rule for the number of cells in the
ring.


b. How many cells are in the honeycomb after the ninth ring is formed?

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Answer:

Part B is 271!!!

Step-by-step explanation:

a9=54

S9=9/2(6+54)=270

270+1

=271

By plugging in the ring number, 9, in the equation for the number of

cells in a ring, gives 54.

Response:

A. The rule for the number of cells in the ring is, aₙ = 6 + (n - 1) × 6

B. The number of cells in the ninth ring are 54 cells

How can the number of cells be expressed as an arithmetic sequence?

Given;

The type of sequence = Arithmetic sequence

From the possible drawing of the question obtained from a similar question, we have;

Number of cells in the first ring that goes around the first cell = 6

Number of cells that go around the second ring = 12

A. The common difference of the arithmetic sequence = 12 - 6 = 6

We have that the nth term of an arithmetic sequence is; aₙ = a + (n - 1)·d

Taking the first ring as the first term, we have;

a = 6

Which gives;

The rule for the number of cells in the ring is, aₙ = 6 + (n - 1) × 6

Where;

n = The ring number

B. In the ninth ring, we have;

a₉ = 6 + (9 - 1) × 6 = 54

  • The number of cells in the ninth ring, a₉ = 6 + (9 - 1) × 6 = 54

Learn more about arithmetic sequence here:

https://brainly.com/question/773011

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