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If a constant is added or subtracted from each term of an A.P. then resulting sequence is also an A.P.

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in Mathematics - Class 11 by (789k points)
If a constant is added or subtracted from each term of an A.P. then resulting sequence is also an A.P.

(a) True

(b) False

The question was posed to me in unit test.

This question is from Arithmetic Progression(A.P.) in chapter Sequences and Series of Mathematics – Class 11

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The correct answer is (a) True

Explanation: Let x be the constant which is added to each term of an A.P., then an’ = an + x and a’ = a + x. So n^th term will be an’ = an + x = a+(n-1) d + x = (a + x) + (n-1) d = a’ + (n-1) d which is n^th term of an A.P. If x is negative it is case of subtraction.

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