The sum of the first three terms of an AP is 33. If the product of the first and the third term exceeds the second term by 29, find the AP
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,
Let the three terms in AP be a - d, a, a + d.
a - d + a + a + d = 33
a = 11.
(a - d) (a + d) = a + 29.
Since, a² - b² = (a + b)(a - b), we have,
a² - d² = a + 29
121 - d² = 11 + 29
d² = 81
d = ± 9
Hence, there will be two APs
They are 2, 11, 20, ... and 20, 11, 2, ...
Therefore, the two APs are 2, 11, 20, ... and 20, 11, 2, ...
✦ Try This: If Sₙ denotes the sum of first n terms of an A.P., prove that S₃₀ = 3[S₂₀ - S₁₀]
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5
NCERT Exemplar Class 10 Maths Exercise 5.3 Sample Problem 3
The sum of the first three terms of an AP is 33. If the product of the first and the third term exceeds the second term by 29, find the AP
Summary:
The sum of the first three terms of an AP is 33. If the product of the first and the third term exceeds the second term by 29, the AP is 2, 11, 20, ... and 20, 11, 2, ...
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