## 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)

Solution:

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

Solution:

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

Solution:

(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:
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