Question

What is the sum of the first n terms of this sequence 3,4,5,6,7.///

Answer 1

`a_1=3\\a_2=3+1=4\ (a_1+1)\\a_3=4+1=5\ (a_2+1)\\a_4=5+1=6\ (a_3+1)\\a_5=6+1=7\ (a_4+1)\\\\it's\ an\ arithmetic\ sequence\ where\ a_1=3\ and\ d=1\\\\formula\ for\ the\ sum\ of\ the\ first\ n\ terms:\ S_n=(2a_1+(n-1)d)/(2)\cdot n\\\\therefore\\\\S_n=(2\cdot3+(n-1)\cdot 1)/(2)\cdot n=(6+n-1)/(2)\cdot n=(5+n)/(2)\cdot n=(5+n)/(2)\cdot(n)/(1)=\boxed{(5n+n^2)/(2)}`