Constant is subtracted from each term of an A.P. the resulting sequence is also an ______

Geometric Sequence

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Arithmetic Progression

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Both A and B

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None of the above

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Solution

The correct option is A Arithmetic Progression
If a constant is subtracted from each term of an A.P. the resulting sequence is also an arithmetic progression.

For example : Let the sequence be ${a_{1}, a_{2}, a_{3} . . . . . . a_{4}}$ be an arithmetic progression with common difference $d$ .

Again subtract $k$ to the above sequence.

Then the resulting sequence is $a_{1} - k, a_{2} - k, a_{3} - k . . . . . .$ be an A.P.

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Similar questions

Q. If a constant is added to each term of an A.P. the resulting sequence is also an ______

State true or false For any arithmetic progression, when a fixed number is added or subtracted to each term, the resulting sequence still remains an A.P. with the common difference remaining unchanged.

Q. Prove:

If each term of an A.P. is divided by a non-zero constant then the resulting sequence is also an A.P.

Q. Three arithmetic terms are inserted between two number a and b. The resulting sequence is a/an ___.

Q. p, r, s, t, u
An arithmetic sequence is a sequence in which each term after the first is equal to the sum of the preceding term and a constant. If the list of letters shown above is an arithmetic sequence, which of the following must also be an arithmetic sequence?
I. 2p, 2r, 2s, 2t, 2u
II. p-3, r-3, s-3, t-3, u-3
III.

p^{2}, r^{2}, s^{2}, t^{2}, u^{2}

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