Chapter 13.3, Problem 44STP

To determine

The value of the f .

Answer to Problem 44STP

The value of the f is 146 and the correct option is c.

Explanation of Solution

Given:

The variables a,b,c,d and f are integers in sequence.

Here, a=2 and b=12.

For evaluating the next number, doubling the last term and adding that will result one less than the next to last term.

Options given are:

  $\begin{array}{l}A74\\ B144\\ C146\\ D256\end{array}$

Since, a,b,c,d and f are in sequence.

  a=2 and b=12.

Now, the next term is evaluated as:

Double the last term:

  $2\left(b\right)=2\left(12\right)=24$

One less than the next to last term:

  $a-1=2-1=1$

Adding the above result:

  $\begin{array}{l}24+1=25\\ c=25\end{array}$

Similarly:

Double the last term:

  $2\left(c\right)=2\left(25\right)=50$

One less than the next to the last term:

  $b-1=12-1=11$

Now, adding the above two numbers:

  $\begin{array}{l}50+11=61\\ d=61\end{array}$

Similarly,

  $\begin{array}{l}2\left(d\right)=2\left(61\right)=122\\ \Rightarrow c-1=25-1=24\\ \Rightarrow 122+24=146\\ f=146\end{array}$

Hence, the correct option is c.