Advertisements
Advertisements
Question
If numbers n – 2, 4n – 1 and 5n + 2 are in A.P., find the value of n and its next two terms.
Advertisements
Solution
Since (n – 2), (4n – 1) and (5n + 2) are in A.P., we have
(4n – 1) – (n – 2) = (5n + 2) – (4n – 1)
`\implies` 4n – 1 – n + 2 = 5n + 2 – 4n + 1
`\implies` 3n + 1 = n + 3
`\implies` 2n = 2
`\implies` n = 1
∴ (n – 2), (4n – 1) and (5n + 2)
∴ (1 – 2), (4(1) – 1) and (5(1) + 2)
So, the given numbers are –1, 3, 7
`\implies` a = –1 and d = 3 – (–1) = 4
Hence, the next two terms are (7 + 4) and (7 + 2 × 4)
i.e 11 and 15
APPEARS IN
RELATED QUESTIONS
If the 3rd and the 9th terms of an AP are 4 and –8 respectively, which term of this AP is zero?
Find the sum of all integers between 84 and 719, which are multiples of 5.
How many two-digits numbers are divisible by 3?
Find the first term and common difference for the following A.P.:
5, 1, –3, –7, ...
Find the first term and common difference for the A.P.
0.6, 0.9, 1.2,1.5,...
The common difference of the A.P. is \[\frac{1}{2q}, \frac{1 - 2q}{2q}, \frac{1 - 4q}{2q}, . . .\] is
Suppose three parts of 207 are (a − d), a , (a + d) such that , (a + d) >a > (a − d).
The sum of the first 2n terms of the AP: 2, 5, 8, …. is equal to sum of the first n terms of the AP: 57, 59, 61, … then n is equal to ______.
The middle most term(s) of the AP: -11, -7, -3,.... 49 is ______.
The first term of an AP of consecutive integers is p2 + 1. The sum of 2p + 1 terms of this AP is ______.
