Sequences and Series

The $6$6th term of a geometric sequence is $557$557 and the $13$13th term is $255642$255642.

a

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.

b

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.

c

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 |
$=$= | $\editable{}$ |

d

Hence determine the $8$8th term of the sequence.

Give your answer to the nearest integer.

Easy

Approx 4 minutes

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