Question

10.03 Quiz: Geometric Sequences here is the answers

Answer 1

Answer:

Step-by-step explanation:

1). $a_1=\frac{2}{5}$

  $a_n=5a_{n-1}$

  Since, recursive formula for a geometric sequence is given by,

  $a_n=r.a_{n-1}$

  Here, r = common ratio

  Comparing both, value of r = 5

  Explicit formula of the sequence is given by,

  $a_n=a_1(r)^{n-1}$

  Therefore, explicit formula will be,

  $a_n=\frac{2}{5}(5)^{n-1}$

2). Given recursive formula is,

   $a_n=\frac{1}{2}(\frac{4}{3})^{n-1}$

   By comparing this formula with the standard recursive formula for geometric sequence,

   $a_n=a_1(r)^{n-1}$

   $a_1=\frac{1}{2}$

   $r=\frac{4}{3}$

  Therefore, recursive formula for the sequence will be,

   $a_1=\frac{1}{2}$

   $a_n=a_{n-1}(\frac{4}{3})$

3). Let the explicit formula is,

    $a_n=a_1(r)^{n-1}$

    For 2 years of investment, $a_n=550000$, $a_1=500000$ and n = 2

    550000 = $500000(r)^{2-1}$

    $r=\frac{550000}{500000}$

    r = 1.1

    Therefore, explicit formula will be.

    $a_n=500000(1.1)^{n-1}$

    Option (3) is the answer.

4). Explicit formula for a geometric sequence is,

   $a_n=a_1(r)^{n-1}$

   Here $a_1$ = First term

   r = common ratio

   from the given sequence,

   $a_1$ = 9

   r = $\frac{a_2}{a_1}$

   r = $\frac{6}{9}=\frac{2}{3}$

   Explicit formula will be,

   $a_n=9(\frac{2}{3})^{n-1}$

5). Recursive formula of a geometric sequence is given by,

   $a_1$ = First term of the sequence

   $a_n=a_{n-1}(r)$

   From the given sequence,

   $a_1=4$

   r = $\frac{-16}{4}=-4$

   Therefore, recursive formula will be,

   $a_1=4$

   $a_n=a_{n-1}(-4)$ = $-4a_{n-1}$