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## Tamilnadu Samacheer Kalvi 8th Maths Solutions Term 2 Chapter 4 Information Processing Ex 4.1

Question 1.

Choose the correct answer:

Question (i)

What is the eleventh Fibonacci number?

(a) 55

(b) 77

(c) 89

(d) 144

Answer:

(c) 89

Hint:

∴ 11th Fibonacci number is 89

Question (ii)

If F(n) is a Fibonacci number and n = 8, which of the following is true?

(a) F(8) = F(9) + F(10)

(b) F(8) = F(7) + F(6)

(c) F(8) = F(10) x F(9)

(d) F(8) = F(7) – F(6)

Answer:

(b) F(8) = F(7) + F(6)

Hint:

Given F(n) is a Fibonacci number & n = 8

F(8) = F(7) + F (6) as any term in Fibonacci series is the sum of preceding 2 terms

Question (iii)

Every 3^{rd} number of the Fibonacci sequence is a multiple of ………..

(a) 2

(b) 3

(c) 5

(d) 8

Answer:

(a) 2

Hint:

Every 3rd number in Fibonacci sequence is a multiple,of 2

Question (iv)

Every ……….. number of the Fibonacci sequence is a multiple of 8

(a) 2^{nd}

(b) 4^{th}

(c) 6^{th}

(d) 8^{th}

Answer:

(c) 6^{th}

Question (v)

The difference between the 18th and 17th Fibonacci number is

(a) 233

(b) 377

(c) 610

(d) 987

Answer:

(d) 987

Hint:

F(18) = F(17) + F (16)

F(18) – F(17) = F(16) = F(15) + F(14) = 610-377 = 987

Question 2.

In the given graph sheet draw and colour how the Fibonacci number pattern makes a spiral in the Golden Rectangle.

Steps:

As per the instruction given, draw squares of side equal to each term of Fibonacci number – starting with 1 x 1 square, 2 x 2 square, 3 x 3 square and so on.

For spiral:

Starting from 1st square, join opposite diagonal points in a curve in all the squares to form a spiral.