Arithmetic Sequence Worksheet Solution6

In the page arithmetic sequence worksheet solution6 you are going to see solution of each questions from the arithmetic sequence worksheet.

(17) If a , b , c are in A.P then prove that (a - c)^2 = 4(b^2 - ac)     


Since a, b, c are in A.P so

                       b – a = c – b

                      b + b = c + a

                         2 b = c + a

  Taking squares on both sides

                      (2 b) ² = (c + a)²

                      4b² = (c + a)²

Subtracting by 4ac on both sides, we get

                4b² – 4ac  = (c + a)² – 4 ac

                4(b² – ac)  = c² + a² + 2 ac – 4 ac

                4(b² – ac)  = c² + a² - 2 ac

                4(b² – ac)  = ( c – a )²

(18) If a , b , c are in A.P then prove that (1/bc),(1/ca),(1/ab) are also in A.P


a , b , c are in A.P

Divide each term by abc, so we get

(a/abc),(b/abc),(c/abc) are also an A.P

By simplifying this we get,

(1/bc),(1/ca),(1/ab) are also in A.P

(19) If a²,b²,c² are in A.P, then show that 1/(b+c) , 1/(c+a) , 1/(a+b) are also in A.P


(20) If a^x = b^y = c^z, x ≠ 0 , y ≠ 0 , z ≠ 0 and b² = ac then show that 1/x,1/y and 1/z are in A.P

Quote on Mathematics

“Mathematics, without this we can do nothing in our life. Each and everything around us is math.

Math is not only solving problems and finding solutions and it is also doing many things in our day to day life.  They are: 

It subtracts sadness and adds happiness in our life.    

It divides sorrow and multiplies forgiveness and love.

Some people would not be able accept that the subject Math is easy to understand. That is because; they are unable to realize how the life is complicated. The problems in the subject Math are easier to solve than the problems in our real life. When we people are able to solve all the problems in the complicated life, why can we not solve the simple math problems?

Many people think that the subject math is always complicated and it exists to make things from simple to complicate. But the real existence of the subject math is to make things from complicate to simple.”

arithmetic sequence worksheet solution6 arithmetic sequence worksheet solution6