## Arithmetic Sequence Worksheet Solution6

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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:

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