What-is-the-sum-of-ten-odd-numbers-and-eleven-even-numbers-

Question Number 53515 by 0955083339 last updated on 22/Jan/19

What is the sum of ten odd numbers

and eleven even numbers ?

Answered by tanmay.chaudhury50@gmail.com last updated on 23/Jan/19

S_{o d d} = 1 + 3 + 5 + \dots + [1 + (10 - 1) 2]

S_{o d d} = 1 + 3 + 5 + \dots + 19

S_{o d d} = 19 + 17 + 15 + \dots + 1

a d d

2 S_{o d d} = 20 + 20 + 20 \dots t e n t i m e s

2 S_{o d d} = 20 \times 10

S_{o d d} = 100

o r d i r e c t f o r m u l a

S = \frac{n}{2} [2 a + (n - 1) d]

= \frac{10}{2} [2 \times 1 + (10 - 1) 2]

= 100

S_{e v e n} = 2 + 4 + 6 + \dots + [2 + (11 - 1) 2]

S_{e v e n} = 2 + 4 + 6 + \dots + 22

S_{e v e n} = 22 + 20 + 18 + \dots + 2

a d d

2 S_{e v e n} = 24 + 24 + 24 \dots e l e v e n t i m e s

2 S_{e v e n} = 24 \times 11

S_{e v e n} = \frac{24 \times 11}{2} = 132

o r d i r e c t f o r m u l a

S_{e v e n} = \frac{11}{2} [2 \times 2 + (11 - 1) 2]

S_{e v e n} = \frac{11}{2} [24] = 132