Question

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

Given, a_n = -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 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 15^th term will be

a₁₅ = -4(15) + 15 = -60 + 15 = -45