Question

find S78 for sequence of odd natural numbers from 1 to 33​

Answer 1

1 + 3 + 5 + ... + (2n-1) = ?

The sum of the first n numbers of an arithmetic sequence can be derived from this formula

The values of a, d and n are:

a = 1 (the first term)

d = 2(the “common difference” between terms)

n = 3(how many terms to add up)

Therefore, the sum of the first 3 odd numbers becomes

S = (n/2) * (2a + (n - 1)d)

= (3/2) * (2 * 1 + (3 - 1)2)

= (3/2) * (2 + 2 * 2)

= (3/2) * (2 + 4)

= (3/2) * 6

= 3 * 3

= 9

Let’s prove if it works

X₁ = 1

X₂ = 1 + 3 = 4 = 2²

X₃ = 1 + 3 + 5 = 9 = 3²

From this, the answer seems to be

1 + 3 + 5 + ... + (2n-1) = n²

Let’s put that into code

>>>>>>>>>>>>>> Ruby <<<<<<<<<<<<<<<<

def sum_odd_numbers(n)

puts n ** 2

end