Advertisements
Advertisements
Question
If a, b and c are in A.P. show that 4a, 4b and 4c are in A.P.
Solution
a, b and c are in A.P.
`=>` b – a = c – b
`=>` 2b = a + c
Given terms are 4a, 4b and 4c
Now 4b – 4a = 2(2b – 2a)
= 2(a + c – 2a)
= 2(c – a)
And 4c – 4b = 2(2c – 2b)
= 2(2c – a – c)
= 2(c – a)
Since 4b – 4a = 4c – 4b, the given terms are in A.P.
APPEARS IN
RELATED QUESTIONS
Find the 50th term of the sequence:
`1/n, (n + 1)/n, (2n + 1)/n,..........`
How many terms are there in the series 4, 7, 10, 13, ........,148?
Which term of the series:
21, 18, 15 ....... is –81?
Can any term of this series be zero? If yes, find the number of terms.
The sum of the 2nd term and the 7th term of an A.P is 30. If its 15th term is 1 less than twice of its 8th term, find the A.P
Which term of the A.P. 5, 15, 25, .......... will be 130 more than its 31st term?
Which of the following lists of numbers form an A.P.? If they form an A.P., find the common difference d and write the next three terms : – 2, 2, – 2, 2,…..
Which of the following lists of numbers form an A.P.? If they form an A.P., find the common difference d and write the next three terms : `sqrt(2), sqrt(8), sqrt(18), sqrt(32)`,...
Which of the following lists of numbers form an A.P.? If they form an A.P., find the common difference d and write the next three terms : `3, 3 + sqrt(2), 3 + 2sqrt(2), 3 + 3sqrt(2)`,...
The 24th term of an A.P. exceeds its 19th term by 10, its common difference is ______.
The nth term of an A.P. is 7n – 5. Its common difference is ______.
