Chapter SH, Problem 7.32EP

To determine

To find next three term of the sequence $48,-96,192,-384,\mathrm{768......}.$

Answer to Problem 7.32EP

Sixth term is -1536

Seventh term is 3072

Eighth term is -6144

Explanation of Solution

Given information:

The sequence $48,-96,192,-384,\mathrm{768......}.$

Formula used:

  $a_n=a{r}^{n-1}$

where as,

  $a_n$ is the n^th term of the geometric sequence

  a is first term in geometric sequence

  r is common ratio of the geometric sequence

Calculation:

The sequence $48,-96,192,-384,\mathrm{768......}.$

  $a=a_1=48$

  $a_2=-96$

Common ratio

  $r=\frac{-96}{48}$

On solving,

  $r=-2$

Using formula to calculate sixth, seventh, and eighth term of sequence

  $a_6=a{r}^5$

On putting a and r

  $a_6=48{(-2)}^5$

On solving,

  $a_6=-1536$

Then, sixth term is -1536

  $a_7=a{r}^6$

On putting value of a and r

  $a_7=48{(-2)}^6$

On solving,

  $a_7=3072$

Then, seventh term is 3072

  $a_8=a{r}^7$

On putting value of a and r

  $a_8=48{(-2)}^7$

On solving,

  $a_8=-6144$

Then, eighth term is -6144