A-Level Edexcel Maths Pure Functions: Ann has some sticks that are all

Question

Ann has some sticks that are all of the same length. She arranges them in squares and has made the following 3 rows of patterns:

Row 1  ☐
Row 2  ☐☐
Row 3  ☐☐☐

She notices that 4 sticks are required to make the single square in the first row, 7 sticks to make 2 squares in the second row and in the third row she needs 10 sticks to make 3 squares.

(a) Find an expression, in terms of n, for the number of sticks required to make a similar arrangement of n squares in the rth row.

(b) Ann continues to make squares following the same pattern. She makes 4 squares in the 4th row and so on until she has completed 10 rows.

(c) Find the total number of sticks Ann uses in making these 10 rows.

(d) Ann started with 1750 sticks. Given that Ann continues the pattern to complete k rows but does not have sufficient sticks to complete the (k + 1)th row,

e) show that k satisfies $k(3 - 100) + (k + 35) < 0.$

(f) Find the value of k.

Ann has some sticks that are all of the same length - Edexcel - A-Level Maths Pure - Question 10 - 2007 - Paper 2

Worked Solution & Example Answer:Ann has some sticks that are all of the same length - Edexcel - A-Level Maths Pure - Question 10 - 2007 - Paper 2

Find an expression, in terms of n, for the number of sticks required to make a similar arrangement of n squares in the rth row.

Find the total number of sticks Ann uses in making these 10 rows.

show that k satisfies $k(3 - 100) + (k + 35) < 0.$

Find the value of k.

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