In the infinite sequence a,a1,a2,a3...an each term after the first is equal to twice the previous term. If a5-a2=12 what is the value of a1?
Please explain if this applies to arithmetic progression. How do I work this problem out?
This is not an arithmetic progression. In an arithmetic progression the difference between 2 consecutive terms of the sequence remains constant
This is not the case with this particular question.
This is a geometric progression. In a geometric progression the ratios between two consecutive terms of the sequence remains constant. Here a2/a1 = 2/1; a3/a2=2/1; so on and so forth
Now a5-a2 = 12
If a1 is x then a2 = 2x,a3=4x,a4=8x,a5=16x
So 16x - 2x = 12
14x=12
Hence x = 12/14 = 6/7
Thus the first term is 6/7
