a, 2a + 1, 3a + 2, 4a + 3,... 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.
a₁ = a
a₂ = 2a + 11
a₃ = 3a + 21
a₄ = 4a + 3
Calculating the difference, we get,
a₂ - a₁ = 2a + 11 - a = a + 1
a₃ - a₂ = 3a + 21 - 2a + 11 = a + 1
a₄ - a₃ = 4a + 3 - 3a + 21 = a + 1
Therefore, a₂ - a₁ = a₃ - a₂ = a₄ - a₃
Each successive term of the given list has the same difference.
Therefore, it forms an AP.
The next three terms are,
a₅ = a + 4d = a + 4(a + 1) = 5a + 4
a₆ = a + 5d = a + 5(a + 1) = 6a + 5
a₇ = a + 6d = a + 6(a + 1) = 7a + 6
Therefore, it forms an AP and the next three terms are 5a + 4, 6a + 5 and 7a + 6.
✦ Try This: The general term of a sequence is given by an = -4n + 15. Is the sequence an A. P.? If so, find its 15th term and the common difference
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5
NCERT Exemplar Class 10 Maths Exercise 5.3 Problem 2 (v)
a, 2a + 1, 3a + 2, 4a + 3,... verify that the following is an AP, and then write its next three terms
Summary:
a, 2a + 1, 3a + 2, 4a + 3,...forms an A.P and the next 3 terms are 5a + 4, 6a + 5,7a + 6
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