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# Problem 3: The general term of a sequence is given by an = -4n + 15. Is the sequence an A.P.? If so, find its 15th term and the common difference.

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This is arithmetic progression based question from Chapter name- Arithmetic Progression
Chapter number- 9
Exercise – 9.2

In this question,  we have the general term of a sequence an = -4n + 15.

Now we have t find out that if the sequence is an A.P. If so, then we have to find its 15th term and the common difference.

CBSE DHANPAT RAI PUBLICATIONS
Understanding CBSE Mathematics
Class :- 10th
Question no 3

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1. Given:

an = -4n + 15

Now putting n = 1, 2, 3, 4 we get,

a1 = -4.(1) + 15 = -4 + 15 = 11

a2 = -4.(2) + 15 = -8 + 15 = 7

a3 = -4.(3) + 15 = -12 + 15 = 3

a4 = -4.(4) + 15 = -16 + 15 = -1

We can see that,

a2 – a1 = 7 – (11) = -4

a3 – a2 = 3 – 7 = -4

a4 – a3 = -1 – 3 = -4

Since, the successive difference of list is same i.e -4

∴ The given sequence is in A.P and have common difference of -4

Hence, the 15th term will be

a15 = -4(15) + 15 = -60 + 15 = -45

And, a15 = -45

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