AP GP Basic Quiz

The sequence

 $8,\ \frac{8}{3},\ \frac{8}{9},\frac{8}{27},...$  represents a ________________

• Geometric progression with common ratio 3.

• Arithmetic progression with common difference  $\frac{1}{3}$ . 

• Geometric progression with common ratio  $\frac{1}{3}$  .

• sequence that is neither an arithmetic nor geometric.

The sequence

 $2,-4,-10,...$  represents ___________________

• a sequence that is neither arithmetic nor geometric.

• a convergent sequence.

• a geometric progression with common ratio  $-2$ . 

• an arithmetic progression with common difference  $-6$ .

Which of the following is used to prove that a sequence

 $\left\{u_n\right\}$  is an arithmetic progression?

•  $u_3$  and  $u_2$  has the same difference as  $u_2$ and $u_1$ . 

•  $u_n-u_{n-1}=d$  , where  $d$  is a constant.

•  $\frac{u_n}{u_{n-1}}=d$  , where  $d$  is a constant.

•  $u_3$  and  $u_2$  has the same ratio as  $u_2$  and $u_1$ . 

The 20th term of the arithmetic progression

 $\left\{4,12,20,...\right\}$  is 

The sum of the first 100 terms of the arithmetic progression

 $\left\{4,12,20,...\right\}$  is

Given a geometric progression with first term 5 and common ratio

 $\frac{1}{3}$  , find the value of the 7th term to 3 s.f.

Given a geometric progression with first term 5 and common ratio 

 $\frac{1}{2}$  , find sum of the first 10 terms to 3 s.f.

Given a geometric progression with first term 5 and common ratio 

 $\frac{1}{2}$  , find sum of to infinity

A geometric series is convergent if

• $r<1$

• $r>1$

• $-1\le r\le1$

• $-1<r<1$

An arithmetic series is always divergent. True or False?

• True

• False

• It depends on the common difference.

• It is divergent only when $\left|d\right|>1$ .