86.9k views
3 votes
I need help with this plz help me

I need help with this plz help me-example-1

1 Answer

6 votes

Answer:

Please check the explanation.

Explanation:

1) Writing the equation of the pattern

Figure 1 has 4 circles.

Figure 2 has 7 circles.

Figure 3 has 10 circles.

Thus, the sequence becomes

4, 7, 10,...

Finding the common difference between the adjacent terms

d = 7 - 4 = 3, d = 10 - 7 = 3

As the common difference is the same, so this represents the Arithmetic sequence.

so

d = 3

as

a₁ = 4

Thus, the nth term of the Arithmetic sequnce is

aₙ = a₁ + (n-1)d

aₙ = 4 + (n-1)3

aₙ = 4 + 3n - 3

aₙ = 1 + 3n

2) Determining the circles in the 23rd figure

As the nth term is given by

aₙ = 1 + 3n

putting n = 23

a₂₃ = 1 + 3(23)

a₂₃ = 1 + 69

a₂₃ = 70

3) Determining the figure having 82 circles

As the nth term is given by

aₙ = 1 + 3n

Given

aₙ = 82

To determine

n=?

Thus,

aₙ = 1 + 3n

82 = 1 + 3n

3n = 82-1

3n = 81

Dividing both sides by 3

n = 27

Therefore, 27th figure will have 82 circles.

User Jay Rajput
by
8.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.