CameraIcon

SearchIcon

MyQuestionIcon

1

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

Common Difference

If a, b and c...

Question

If a, b and c are in A. P. show that :

(i) 4a , 4b and 4c are in A.P.

(ii) a + 4, b +4 and c + 4 are in A.P.

Open in App

Solution

a) a, b and c are in A. P
Therefore b-a=c-b
Similarly
4b-4a=4c-4b
4(b-a)=4(c-b)
b-a=c-b
Hence proved

b) b + 4 -(a+4) = b + 4 -a- 4 = b - a

c + 4 -(b+4) = c + 4 -b- 4 = c - b

a + 4, b +4 and c + 4 are in A.P.
because a, b, c are in A. P

Suggest Corrections

thumbs-up

21

Similar questions

Q. If a,b,c are in A.P., then show that :
(i)

a^{2} (b + c), b^{2} (c + a), c^{2} (a + b)

are also in A.P.
(ii)

b + c - a, c + a - b, a + b - c

are in A.P.
(iii)

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

a, b

c

are in A.P. Show that :

(b + c - a), (c + a - b)

(a + b - c)

are also in A.P.

a, b, c

are in A.P., then show that:
(i)

a^{2} (b + c), b^{2} (c + a), c^{2} (a + b)

are also in A.P.
(ii)

b + c - a, c + a - b, a + b - c

Q. Three numbers

a, b, c

4 a, 5 b

4 c

are in A.P. and

a + b + c = 70,

| c - a |

a, b, c

G . P .

4 a, 5 b, 4 c

are in A.p. such that

a + b + c = 70

, then value of

b

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Introduction to AP

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Common Difference

Standard X Mathematics

Join BYJU'S Learning Program

CrossIcon