0, 1/4 , 1/2 , 3/4 ,... verify that the following is an AP, and then write its next three terms
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 above, we have,
d = ¼ - 0 = ¼
a₁ = 0
a₂ = 1/4
a₃ = 1/2
a₄ = 3/4.
Calculating the difference, we get,
a₂ - a₁ = 1/4
a₃ - a₂ = 1/2 - 1/4 = 1/4
a₄ - a₃ = 3/4 - 1/2 = 1/4
As, a₂ - a₁ = a₃ - a₂ = a₄ - a₃, it forms an AP.
Hence, each successive term of the given list has the same difference,
Therefore, it forms an AP.
The next three terms are,
a₅ = a + 4d = 0 + 4(¼) = 1
a₆ = a + 5d = 0 + 5(¼) = 5/4.
a₇ = a + 6d = 0 + 6(¼) = 3/2.
✦ Try This: The 10th and 18th terms of an A. P. are 41 and 73 respectively. Find 26th term
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5
NCERT Exemplar Class 10 Maths Exercise 5.3 Problem 2 (i)
0, 1/4 , 1/2 , 3/4 ,... verify that the following is an AP, and then write its next three terms
Summary:
0, 1/4 , 1/2 , 3/4 ,...forms an A.P and the next 3 terms are 1, 5/4, 3/2
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