Chapter ISG, Problem 3.6.1P

To determine

To evaluate the formula for the given sequence.

Explanation of Solution

Given information:

The sequence is -0.8, -0.5, -0.2, 0.1…

The function is $f(n)=0.3n-0.5$

Formula used:

Athematic sequence formula,

  $a_n=a1+(n-1)d$

Proof:

Substituting the value of $n=1$ , in the given function for the first term,

  $f(1)=(0.3\times 1)-0.5$

On solving,

  $f(1)=-0.2$

The f(1) calculated from the formula is not equal to the first term on the sequence. Therefore, the given function is not the correct function for the equation.

The first term is -0.8

The common difference is,

  $d=-0.5-(-0.8)$

Opening the brackets,

  $d=-0.5+0.8$

On solving,

  $d=0.3$

Substituting the values in the arithmetic sequence formula,

  $a_n=-0.8+(n-1)0.3$

Opening the brackets,

  $a_n=-0.8+0.3n-0.3$

On solving,

  $a_n=-1.1+0.3n$

Hence, the correct function to represent the sequence is,

  $f(n)=-1.1+0.3n$