Question

4 Consider the pattern:
1 = 1 = 1^2
1 + 3 = 4 = 2^2
1 + 3 + 5 = 9 = 3^2
a. Predict the value of 1+3+5+7+9+::::::+99

Answer 1

that may be 50^2

Answer 2

how do you get that though?

Answer 3

(no of terms)^2

Answer 4

@mekaprasantho how did you know it was 50 terms?

Answer 5

there are 50 odd numbers and 50 even numbers 1 - 100
here there are only odd numbers

Answer 6

Is it possible to state that in mathematical terms?

Answer 7

can you?

Answer 8

sum of first 'n' odd natural numbers is n^2

Answer 9

i dont know the proof

Answer 10

99 = 2n-1

solve for n

Answer 11

you can get it easily if you consider it to be an arithmetic progression with a=1,d=2,n=50
sum =n/2[2a+(n-1)d]