If 63 {63}^(2) = 1 + 3 + 5 + ... + k \: then \: k = ​

Question

If 63

`{63}^(2) = 1 + 3 + 5 + ... + k \: then \: k =`
​

Answer 1

125

Explanation:

let's see if we can find a pattern

1 = 1 = 1^2

1 + 3 = 4 = 2^2

1 + 3 + 5 = 9 = 3^2

we are starting to see a pattern here, when we add another term, we find the next integer squared.

we can find this last number in our sequence with 2x-1.

so in the next line we should find 4^2. if we plug 4 into 2x-1 we would expect the last term in the sum to be 7.

1 + 3 + 5 + 7 = 16 = 4^2

so 2*63 -1 = 126 - 1 = 125