Problem Solving

In the infinite sequence 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?

1. 4
2. 24/7
3. 2
4. 12/7
5. 6/7

Where would I start?

my answer is E..

here it goes..

as the question says every term after the first term is twice the previous term .. we need to use this in our calculation..

1st term (a1) = a1
2nd term(a2) = 2(a1) ( twice the previous term)... illy others
3rd term(a3) = 2 a2
4th term(a4) = 2 a3
5th term(a5) = 2 a4


the eqn given : a5- a2=12

a5 in terms of a2 using the explanation above is 8 a2 ( 2( a4)= 2(2a3)=4(2a2))


there fore it will 8a2-a2= 12 which means
a2= 12/7

since
a2 = 2a1 therefore 12/7= 2 a1

hence a1 = 6/7.


regards

Sudhir

Backsolve starting with E.

E is the only answer that satifies a1

ahh sequences...

ok first thing just think about simple numbers and translate it to variables

1----2----4
x----2x----2(2x)

1st term= x
2nd term =2x
3rd term=4x
4th term= 2*4x=8x
5th term=8x*2=16x

5th term- 2nd term= 12
16x-2x=12
14x=12
x=12/14
x= 6/7

Answer E.