Interactive practice questions
The $6$6th term of a geometric sequence is $557$557 and the $13$13th term is $255642$255642.
Write an equation involving $a$a, the first term, and $r$r, the common ratio, of this geometric sequence for the $6$6th term.
Write your answer such that the constant term is by itself on one side of the equation.
Write an equation involving $a$a, the first term, and $r$r, the common ratio, of this geometric sequence for the $13$13th term.
Write your answer such that the constant term is by itself on one side of the equation.
Use the simultaneous solving facility of your calculator to determine the values of $a$a and $r$r. Give the value of $a$a to the nearest integer and give the value of $r$r to one decimal place. Assume $a$a and $r$r are positive.
| $a$a | $=$= | $\editable{}$ |
|---|---|---|
| $r$r | $=$= | $\editable{}$ |
Hence determine the $8$8th term of the sequence.
Give your answer to the nearest integer.
The $7$7th term of a geometric sequence is $353$353 and the $13$13th term is $42$42.
The $5$5th term of a geometric sequence is $11$11 and the $12$12th term is $72$72.
The $4$4th term of a geometric sequence is $33$33 and the $14$14th term is $952$952.