determine which is​ greater, P or Q​, and by how much.

Question

If P=2+4+6+8+...+106 and Q=6+8+10+12+...+108 are sums of arithmetic​ sequences.



Please help me solve this problem the easiest way possible. Ive been stuck on this one math problem for days. I do not understand what im doing wrong. Thank you

Answer 1

Since p and q are arithmetic

Sum of an arithmetic progression =s=n/2(a+l) where n = numbers of term

A= first term

L= last term

For the sum of p

A=2

L=106

N= (106÷2)=53

Sum = 53/2(2+106)

= 53*54= 2862

For the sum of q ;

A= 6

L= 108

N= (108÷2)-2=52

Sum = 52/2(6+108)

=2964

So clearly q>p