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.
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Understanding CBSE Mathematics
Class :- 10th
Question no 3
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