Chapter SH, Problem 7.33EP

To determine

To find next three term of the sequence $150,\text{ 75, 37}\text{.5, 18}\text{.75, 9}\text{.375 }\mathrm{........}$

Answer to Problem 7.33EP

Sixth term is 4.6875

Seventh term is 2.43375

Eighth term is 1.171875

Explanation of Solution

Given information:

The sequence $150,\text{ 75, 37}\text{.5, 18}\text{.75, 9}\text{.375 }\mathrm{........}$

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 $150,\text{ 75, 37}\text{.5, 18}\text{.75, 9}\text{.375 }\mathrm{........}$

  $a=a_1=150$

  $a_2=75$

Common ratio

  $r=\frac{75}{150}$

On solving,

  $r=0.5$

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

  $a_6=a{r}^5$

On putting value of a and r

  $a_6=150{(0.5)}^5$

On solving,

  $a_6=4.6875$

Then, sixth term is 4.6875

  $a_7=a{r}^6$

On putting value of a and r

  $a_7=150{(0.5)}^6$

On solving,

  $a_7=2.34375$

Then, seventh term is 2.43375

  $a_8=a{r}^7$

On putting value of a and r

  $a_8=150{(0.5)}^7$

On solving,

  $a_8=1.171875$

Then, eighth term is 1.171875