Question

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.

Answer 1

an=-4n+15

put n=1

a1=-4(1)+15

a1=11

put n=2

a2=-4(2)+15

a2=7

put n=3

a3=-4(3)+15

a3=3

if it is an ap then d1 must be equal to d2

a2-a1=a3-a2

7-11=3-7

4=4

it is an ap

d=4

a=11

a15=a+14d

a15=11+14(4)

a15=11+56

a15=67