Mathematics
State, true or false: if a, b and c are in A.P. then :
(i) 4a, 4b and 4c are in A.P.
(ii) a + 4, b + 4 and c + 4 are in A.P.
Answer
(i) Given,
a, b and c are in A.P.
We know that,
If each term of an A.P. is multiplied by a constant, then the resulting sequence is also an A.P.
Thus, 4a, 4b and 4c are also in A.P.
Hence, yes the terms 4a, 4b and 4c are in A.P.
(ii) To prove,
a + 4, b + 4 and c + 4 are in A.P., difference between consecutive terms should be same.
⇒ (b + 4) - (a + 4) = (c + 4) - (b + 4)
⇒ b - a + 4 - 4 = c - b + 4 - 4
⇒ b - a = c - b [As, a, b and c are in A.P., thus this equation is correct]
Hence, yes the terms a + 4, b + 4 and c + 4 are in A.P.
Related Questions
If numbers n - 2, 4n - 1 and 5n + 2 are in A.P., find the value of n and its next two terms.
Determine the value of k for which k2 + 4k + 8, 2k2 + 3k + 6 and 3k2 + 4k + 4 are in A.P.
An A.P. consists of 57 terms of which 7th term is 13 and the last term is 108. Find the 45th term of this A.P.
4th term of an A.P. is equal to 3 times its first term and 7th term exceeds twice the 3rd term by 1. Find the first term and the common difference.