Arithmetic Progression
Maharashtra Board · Class 10 · Mathematics
Most important questions from Arithmetic Progression for Maharashtra Board Class 10 Mathematics board exam 2026. MCQs, short answer, and long answer questions with marks.
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Sample Questions
Which of the following sequences are arithmetic progressions?
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3, 6, 9, 12, ..., 5, 5, 5, 5, ..., -2, -5, -8, -11, ...
A.P. has constant common difference. (1) d=3, (2) d=0, (4) d=-3 are A.P. (3) is squares (not constant difference), (5) is G.P. (ratio=3).
Which statements about arithmetic progressions are correct?
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Common difference can be negative, Common difference can be zero, The middle term is average of first and last terms
d can be negative (decreasing A.P.), zero (constant A.P.), or positive. Terms can be negative. Middle term = (first + last)/2. Sum may decrease if terms are negative.
The sum of first n natural numbers is given by the formula n(n+1)/2. Find the sum of first 20 natural numbers.
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210
Natural numbers 1, 2, 3, ..., 20 form A.P. with a = 1, d = 1, n = 20. Using formula: Sum = 20(20+1)/2 = 20×21/2 = 210.
In an A.P., if first term is 8 and common difference is -3, find the 6th term.
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-7
a = 8, d = -3, n = 6. Using tn = a + (n-1)d, t6 = 8 + (6-1)(-3) = 8 + 5(-3) = 8 - 15 = -7.
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