Question

If a non-zero number is added to each term of a arithmetic progression is the resulting sequence also in A-p? Justify your​

Answer 1

Answer:

We are adding the same non zero number to every term of that AP. So it will have the same d[common difference]. So the resulting series will also be an AP

Step-by-step explanation:

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Answer 2

Yes, it will be also an AP.

Step-by-step explanation:

Arithmetic progression : a sequence in which the difference between the consecutive terms is constant.

Consider an AP,

a, a + d, a + 2d, a + 3d, a + 4d, a + 5d, .......... so on,

Having common difference d,

Add n ( a non zero number ) in each term of the sequence,

New sequence will be,

a + n, a + d + n, a + 2d + n, a + 3d + n, a + 4d + n, a + 5d +n, .......... so on,

Since,

(a+d+n)-(a+n)=(a+2d+n)-(a+d+n)=(a+3d+n)-(a+2d+n)=(a+4d+n)-(a+3d+n)=(a+5d+n)-(a+4d+n)..........= d,

That is, in sequence a + n, a + d + n, a + 2d + n, a + 3d + n, a + 4d + n, a + 5d +n, ..........,

Difference between consecutive terms is d ( constant ),

Thus, a + n, a + d + n, a + 2d + n, a + 3d + n, a + 4d + n, a + 5d +n, .........., is also an AP.

Hence, proved...

#Learn more:

The nth term of a sequence is 2n + 3.Is the sequence an A.P? If so, find the 6th term

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