New Zealand
Level 7 - NCEA Level 2

# Geometric Series (using graphics calculators)

## Interactive practice questions

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.

Easy
Approx 4 minutes

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.

### Outcomes

#### M7-3

Use arithmetic and geometric sequences and series

#### 91258

Apply sequences and series in solving problems