Question

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

Answer 1

Solution:

Given, a_n = -4n +15

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

a_1 = -4(1) + 15 = -4 + 15 = 11

a_2 = -4(2) + 15 = -8 + 15 = 7

a_3 = -4(3) + 15 = -12+ 15 = 3

a_4 = -4(4) +15 = -16 + 15 = -1

We can see that,

=> a_2 - a_1 = 7 - (1) = -4

=> a_3 - a_2 = 3 - 7= -4

=> a_4 - a_3 = -4

Since the difference between the terms is common, we can conclude that the given sequence defined by a_n = -4n + 15 is an A.P with common difference of -4,

Hence, the 15th term will be

=> a_15 = -4(15) + 15

=> -60 + 15

=> -45