Question

calculate in head, the sum of the following arithmetic sequence.
i, 51 + 52 +53+ ............+ 70
ii, 1 1/2 + 2 1/2 + ...........+12 1/2
iii, 1/2 + 1 + 1 1/2 + 2+ 2 1/2 +........
12 1/2​

Answer 1

Hey Mate ,

Here is your answer

i ) Use this easy method

1+2+3..10 = 55

11+12+13..+20=155

...

51+52+53..+60 = 555

61+62+63...+70=665

So , The Answer is 555+665 = 500 + 600 + 110 = 1100 + 110 = 1210

ii ) Use this method

Take all the halves ( 1/2 ) out and add 1+2+3..+12

= 55+11+12=66+12=78

Now take the halves . we all now 2 halves = 1

So , 12/2 = 6

Final answer = 78+6=84

iii) Do the same method as ii , but there are some changes

here we have double the havles as ii )

which is 12x2 = 24

Now same method

1+2+3..+12 = 55+11+12=66+12=78

Now take the halves . we all now 2 halves = 1

So , 24/2 = 12

Final Answer= 78+12=90

hope it helps you