Question

Sum of all odd numbers between first 0 and 50 second 100 and 200

Answer 1

Answer:

1) 625

2) 7500

Step-by-step explanation:

1) odd numbers between 0 and 50

1, 3, 5, ......... 49

a = 1, d = 2, last number = 49

an = a + (n-1)d

49 = 1 + (n-1)2

49 - 1 = (n-1)2

48/2 = n - 1

24 = n - 1

n = 24 + 1 = 25

Sum of the odd numbers

$sn = \frac{n}{2} (2a + (n - 1)d) \\ = \frac{25}{2} (2(1) + (25 - 1)2) \\ = \frac{25}{2} (2 + 48) \\ = \frac{25}{2} \times 50 \\ = 25 \times 2 \\ = 625$

1) odd numbers between 100 and 200

101, 103, 105, ......... 199

a = 101, d = 2, last number = 199

an = a + (n-1)d

199 = 101 + (n-1)2

199 - 101 = (n-1)2

98/2 = n - 1

49 = n - 1

n = 49 + 1 = 50

Sum of the odd numbers

$sn = \frac{n}{2} (2a + (n - 1)d) \\ = \frac{50}{2} (2(101) + (50 - 1)2) \\ = 25(202 + 98) \\ = 25 \times 300 \\ = 7500$

hope you get your answer