Shortcuts

Value of nth odd number =2n-1 Value of 46th odd number= 2×46-1 =91 p= 1+2+3+......+87+89+91 =92×23 =2116 p-1= 2115

Sum of first $n$ odd numbers is $n^2$ . Thus the sum of first $46$ odd numbers is equal to $46^2 = 2116 = p$

$p-1 = \boxed{2015}$

The sequence of the first 46 odd numbers is an arithmetic progression of $n=46$ terms with a first term $a=1$ and last term $l = 91$ . Therefore, the sum $p = \dfrac {n(a+l)}2 = \dfrac {46(1+91)}2 = 2116$ and $p-1=\boxed{2115}$ .