## 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

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