Geometric Sequence Problems

1The second term of a geometric sequence is 6, and the fifth term is 48. Determine the sequence.

2The 1st term of a geometric sequence is 3 and the eighth term is 384. Find the common ratio, the sum and the product of the first 8 terms.

3Compute the sum of the first 5 terms of the sequence: 3, 6, 12, 24, 48, ...

4Calculate the sum of the terms of the following geometric sequence:

Geometric Sequence

5Calculate the product of the first 5 terms of the sequence: 3, 6, 12, 24, 48, ...

6John has purchased 20 books. The 1st book cost $1, the 2nd, $2, the 3rd, $4, and the 4th ,$8, and so on. How much did John pay for the 20 books?

7The sides of a square, l, have lines drawn between them connecting adjoining sides with their midpoints. This creates another square within the original and this process is continued indefinitely. Calculate the sum of the areas of the infinite squares.

8Calculate the fraction that is equivalent to 0.18181818...

9Calculate the fraction that is equivalent to 3.2777777...


1

The second term of a geometric sequence is 6, and the fifth term is 48. Determine the sequence.

a2= 6;                 a5= 48;        

 an = ak · r n−k

48 = 6 r5−2 ;          r3 = 8;                r = 2.

a1= a2/r; a1= 6/2= 3.

3, 6, 12, 24, 48, ...


2

The 1st term of a geometric sequence is 3 and the eighth term is 384. Find the common ratio, the sum and the product of the first 8 terms.

a 1 = 3;                 a 8 = 384.   

   Common Ratio              Sum of a Sequence           Product of a Sequence

384 = 3 · r8−1 ;       r7 = 128;        r7 = 27;      r= 2.

S8 = (384 · 2 − 3 ) / (2 − 1) = 765

Product of a Sequence


3

Compute the sum of the first 5 terms of the sequence: 3, 6, 12, 24, 48, ...

Sum of Five Terms in a Sequence


4

Calculate the sum of the terms of the following geometric sequence:

Geometric Sequence

Sum of a Geometric Sequence


5

Calculate the product of the first 5 terms of the sequence: 3, 6, 12, 24, 48, ...

Product of a Sequence


6

John has purchased 20 books. The 1st book cost $1, the 2nd, $2, the 3rd, $4, and the 4th ,$8, and so on. How much did John pay for the 20 books?

a1= 1       r= 2;         n = 20;        Sum of a Sequence

S= (1 · 220−1 − 1) / (2 − 1) = $1,048,575 .


7

The sides of a square, l, have lines drawn between them connecting adjoining sides with their midpoints. This creates another square within the original and this process is continued indefinitely. Calculate the sum of the areas of the infinite squares.

Infinite Squares

Sides and Areas

Sides and Areas

Sequence Solution


8

Calculate the fraction that is equivalent to 0.18181818...

0.18181818...= 0.18 + 0.0018 + 0.000018 + ...

a1= 0.18;             r= 0.01;         Sum of a Geometric Sequence

S= 0.18/(1− 0.01)= 2/11


9

Calculate the fraction that is equivalent to 3.2777777...

3.2777777...= 3.2 + 0.07 + 0.007 + 0.0007 + ...

a1= 0.07          r= 0.1;           

3.2 + 0.07/(1 − 0.1) = 32/10 + 7/90 = 59/18




  •