Question

What is the value of n in the following expression? 1 + 2 + 3 + …. + (n – 1) + n + (n – 1) + ….. + 3 + 2 + 1 = 289

Answer 1

Step-by-step explanation:

1+2+3......+(n-1)+n =n(n+1)/2

1+2+3....+(n-1) = n(n+1)/2 - n

adding both

lhs = n(n+1)/2 + n(n+1)/2 - n = n(n+1) - n

lhs = n^2

therefore, n^2 = 289

n =√289

n = 17