Thread: Sequences and Series

1. Sequences and Series

Hello once again. Im really confused with the two sequences and series question. Can somebody please help me ?

1. The 2nd and 4th terms of a geometric series is 36 an 16 respectively. All the terms are positive. Determine the first term.

2. The floowing series is given :

(x-1) + (x-1)2 + (x-1)3

2.1 for which values of x will the series converge ?

3.
n
Σ(3-4k) = -125
k=1
where k =1. determine the value of n.

2. Re: Sequences and Series

Originally Posted by AzraaBux
Hello once again. Im really confused with the two sequences and series question. Can somebody please help me ?

1. The 2nd and 4th terms of a geometric series is 36 an 16 respectively. All the terms are positive. Determine the first term.
For a geometric sequence, a+ ar+ ar^2+ ar^2+ ..., the 2nd term is ar= 36 and the 4th term is ar^2= 16. Solve those two equations for a and r. You can start by eliminating "a" by dividing one equation by another.

2. The floowing series is given :

(x-1) + (x-1)2 + (x-1)3

2.1 for which values of x will the series converge ?
What you give is NOT an infinite series so there is no question of convergence! Do you mean that the series continues a (x-1)^n? That's a "power series" and you can use the "ratio test" to determine for which values of x it converges.

3.
n
Σ(3-4k) = -125
k=1
where k =1. determine the value of n.
Again, what you have written makes no sense. Your sum has k going from 1 to n so "where k= 1" is meaningless.
Dropping the "where k= 1", just go ahead and do the arithetic. If n= 1, the "sum" is just 3- 4= -1, not -125. If n= 2, the sum is (3- 4)+ (3- 8)= -1- 5= -6. Keep going.