Mathematics
If numbers n - 2, 4n - 1 and 5n + 2 are in A.P., find the value of n and its next two terms.
Answer
Since, n - 2, 4n - 1 and 5n + 2 are in A.P.
Hence, difference between consecutive terms are equal.
∴ 4n - 1 - (n - 2) = (5n + 2) - (4n - 1)
⇒ 4n - n - 1 + 2 = 5n - 4n + 2 - (-1)
⇒ 3n + 1 = n + 3
⇒ 3n - n = 3 - 1
⇒ 2n = 2
⇒ n = 1.
Substituting n in n - 2, 4n - 1 and 5n + 2 we get,
= 1 - 2, 4(1) - 1, 5(1) + 2 ………
= -1, 3, 7, ………
The above A.P. has first term = -1 and common term = 3 - (-1) = 4.
Next two terms = 7 + 4 = 11 and 7 + 2(4) = 15.
Hence, n = 1 and next two terms of the A.P. are 11 and 15.
Related Questions
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Determine the A.P. whose 3rd term is 16 and the 7th term exceeds the 5th term by 12.
Determine the value of k for which k2 + 4k + 8, 2k2 + 3k + 6 and 3k2 + 4k + 4 are in A.P.
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.