You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard X

Mathematics

Properties of GP

The non zero ...

Question

The non zero numbers $a, b$ and $c$ are in $A P$ if we increase $a$ by $2$ , the numbers becomes in $G . P$ . Find the value of $b - a$ .

Open in App

Solution

a, b, c are in AP
$2 b = (a + c)$
$(a + 2), b, c$ are in GP
$b^{2} = (a + 2) (c)$
$c = (2 b - a)$
$b^{2} = (a + 2) (2 b - a)$
$b^{2} - 2 a b - a^{2} + 4 b - 2 a$
$(b - a)^{2} = 2 (2 b - a)$
$(b - a) = \sqrt{2 (2 b - a)}$ .

Suggest Corrections

Similar questions

Q. Three non zero numbers

a, b,

and

c

are in A.P. If we increase

a

1

or increase

c

2,

the numbers become in G.P. Find the value of

b - a

Q. Three non-zero numbers

a, b

and

c

are in A.P.. If increasing

a

1

or increasing

c

2,

then the numbers are in G.P., then the value of

b

Q. Three non-zero numbers

a, b

and

c

are in A.P.. If increasing

a

1

or increasing

c

2,

then the numbers are in G.P., then the value of

b

The sum of three numbers a, b, c in A.P. is 18. If a and b are each increased by 4 and c is increased by 36, the new numbers form a G.P. Find a, b, c.

Q. Assertion :Let three distinct positive real numbers

a, b, c

are in G.P., then

a^{2}, b^{2}, c^{2}

are in G.P. Reason: If we square each term of a G.P., then the resulting sequence is also in G.P.

Join BYJU'S Learning Program

The non zero numbers a,b and c are in AP if we increase a by 2, the numbers becomes in G.P. Find the value of b−a.

a, b, c are in AP2b=(a+c)(a+2),b,c are in GPb2=(a+2)(c)c=(2b−a)b2=(a+2)(2b−a)b2−2ab−a2+4b−2a(b−a)2=2(2b−a)(b−a)=√2(2b−a).

The non zero numbers $a, b$ and $c$ are in $A P$ if we increase $a$ by $2$ , the numbers becomes in $G . P$ . Find the value of $b - a$ .

a, b, c are in AP
$2 b = (a + c)$
$(a + 2), b, c$ are in GP
$b^{2} = (a + 2) (c)$
$c = (2 b - a)$
$b^{2} = (a + 2) (2 b - a)$
$b^{2} - 2 a b - a^{2} + 4 b - 2 a$
$(b - a)^{2} = 2 (2 b - a)$
$(b - a) = \sqrt{2 (2 b - a)}$ .