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5, 14/3 , 13/3 , 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 = 14/3 - 5 = -1/3

a₁ = 5

a₂ = 14/3

a₃ = 13/3

a₄ = 4

Calculating the difference, we get,

a₂ - a₁ = 14/3 - 5 = -1/3.

a₃ - a₂ = 13/3 - 14/3 = -1/3

a₄ - a₃ = 4 - 13/3 = 12-13/3 = -1/3.

As, a₂ - a₁ = a₃ - a₂ = a₄ - a₃, it does not form 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 = 5 + 4 (-⅓) = 11/3

a₆ = a + 5d = 5 + 5(-⅓) = 10/3

a₇ = a + 6d = 5 + 6(-⅓) = 3.

Therefore, it forms an AP and the next three terms are 11/3, 10/3 and 3.

✦ Try This: The sum of 4^th and 8^th terms of an A. P. is 24 and the sum of 6^th and 10^th terms is 34. Find the first term and the common difference of the A. P

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5

NCERT Exemplar Class 10 Maths Exercise 5.3 Problem 2 (ii)

5, 14/3 , 13/3 , 4,... verify that the following is an AP, and then write its next three terms

Summary:

5, 14/3 , 13/3 , 4,...forms an A.P and the next 3 terms are 11/3,10/3,3

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