tmua 2022 Q8

tmua · Uk · paper1 1 marks Geometric Sequences and Series Finite Geometric Sum and Term Relationships

A geometric sequence has first term $a$ and common ratio $r$, where $a$ and $r$ are positive integers and $r$ is greater than 1.
The sum of the first $n$ terms of this sequence is denoted by $S _ { n }$
It is given that the terms of the sequence satisfy
$$S _ { 30 } - S _ { 20 } = k S _ { 10 }$$
for some positive integer $k$.
What is the smallest possible value of $k$ ?

..... 10

A geometric sequence has first term $a$ and common ratio $r$, where $a$ and $r$ are positive integers and $r$ is greater than 1.

The sum of the first $n$ terms of this sequence is denoted by $S _ { n }$

It is given that the terms of the sequence satisfy

$$S _ { 30 } - S _ { 20 } = k S _ { 10 }$$

for some positive integer $k$.

What is the smallest possible value of $k$ ?

Paper Questions

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20