Question

Q2
A = sum of first 10 natural numbers
B = sum of squares of first 10 natural numbers
C = sum of cubes of first 10 natural numbers
D = sum of first 10 even natural numbers
Then the increasing order of A, B, C, D is​

Answer 1

Answer:

A=1+2+3+4+5+6+7+8+9+10 are first 10 natural numbers

=>the first term a=1

the common difference (d) =1

the total number of n terms =10

=>1+2-3+4+5+6+7+8+9+10=55

hence, sum of the first 10 natural numbers =55

B=1^2+2^2+3^2+4^2+5^2+6^2+7^2+8^2+9^2+10^2 are first 10 square numbers

=1+4+9+16+25+36+49+64+81+100

=(1+49)+(4+36)+(8+81)+(16+64)+(25)+(100)

=50+40+90+80+25+100

=100+90+80+50+40+25

=190+80+50+40+25

=270+90+25

=360+25

=385

hence, sum of the squares of first 10 natural numbers =385

C= 1^3+2^3+3^3+4^3+5^3+6^3+7^3+8^3+9^3+10^3 are first 10 cube numbers

=1^3+2^3+3^3+4^3+5^3+6^3-7^3+8^3+

9^3+10^3=(10+11/2)^2=55^ 2=3025

hence, the sum of the cubes of first 10 natural numbers =3025

D=2,4,6,8,10,12,14,16,18,20 are first 10 even numbers

=2+4+6+8+10+13+14+16+18+20=110

hence, sum of first 10 even numbers =110