If the numbers n - 2, 4n - 1 and 5n + 2 are in AP, find the value of n
Solution:
An arithmetic progression (AP) is a sequence where the two consecutive terms have the same common difference. It is obtained by adding the same fixed number to its previous term.
From the question,
n - 2, 4n - 1, 5n + 2 are in AP.
Hence,
(4n - 1) - (n - 2) = (5n + 2) - (4n - 1)
4n - 1 - n + 2 = 5n + 2 - (4n - 1)
(4n - n) + (-1+2) = 5n + 2 - (4n - 1)
3n + 1 = 5n + 2 - (4n - 1)
3n + 1 = 5n + 2 - 4n + 1.
3n + 1 = (5n - 4n) + (2+1)
3n + 1 = 1n + (2+1)
3n + 1 = n + 3
3n - n = 3 - 1
2n = 2
n = 2/2
n = 1.
Therefore, n = 1.
✦ Try This: The sum of the first seven terms of an AP is 182. If its 4th and the 17th terms are in the ratio 1 : 5, find the AP
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5
NCERT Exemplar Class 10 Maths Exercise 5.3 Sample Problem 1
If the numbers n - 2, 4n - 1 and 5n + 2 are in AP, find the value of n
Summary:
An arithmetic progression is a sequence where each term, except the first term, is obtained by adding a fixed number to its previous term. If the numbers n - 2, 4n - 1 and 5n + 2 are in AP, then the value of n is 1
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