Question

Show that a1,a2,a3 ...Form an ap where a n is defined as an= 3+4n

Answer 1

a1=3+4*1=7. a2=3+4*2=11 a3=3+4*3=15. a4=3+4*4=19 and so on..... Now a2-a1=11-7=4. And a3-a2=15-11=4 and a4-a3=19-15=4. From above it is clear that all the terms having same common difference. Hence a1, a2, a3..... are in AP.