Question

10. Consider the following number pattern:
1 + 3 = 4 = 2 = (1 + 1)²
1 + 3 + 5 =9= 32 = (2+1)²
1 + 3 + 5 + 7 = 16 = 42 = (3 + 1)²
1 + 3 + 5 + 7 + 9 = 25 = 5² = (4 + 1)²
1 + 3 + 5 + 7 + ... + a = b = c² = (d + 1)²
(1) Write down the 5th line in the pattern. (2) Given that b = 169, find the values of a, c and d.​

Answer 1

Answer:

a≈13

b≈169

c≈13

d≈12

the above are correct answers.

Answer 2

Answer

10. Consider the following number pattern:

1 + 3 = 4 = 2 = (1 + 1)²

1 + 3 + 5 =9= 32 = (2+1)²

1 + 3 + 5 + 7 = 16 = 42 = (3 + 1)²

1 + 3 + 5 + 7 + 9 = 25 = 5² = (4 + 1)²

1 + 3 + 5 + 7 + ... + a = b = c² = (d + 1)²

(1) Write down the 5th line in the pattern. (2) Given that b = 169, find the values of a, c and d.