Question

Vicki started jogging the first time she ran she ran 3/16 mile the second time she ran 3/8 mile and the third time she ran 9/16 mile if she continued this pattern when was the first time she ran more that 1 mile explain

Answer 1

Answer:

Jogging 6th time.

Step-by-step explanation:

We have been given that Vicki started jogging the first time she ran she ran 3/16 mile the second time she ran 3/8 mile and the third time she ran 9/16 mile.

We can see that the distance Vicki covers each time forms a arithmetic sequence, where 1st term is 3/16.

We know that an arithmetic sequence is in form $a_n=a_1+(n-1)d$, where,

$a_n$ = nth term of sequence,

$a_1$ = 1st term of sequence,

n =  Number of terms in sequence,

d = Common difference.

Let us find common difference of our given sequence as:

$\frac{3}{8}-\frac{3}{16}\Rightarrow \frac{6}{16}-\frac{3}{16}=\frac{3}{16}$

Since Vicki needs to cover more than 1 mile, so we nth term of sequence should be greater than 1.

$1$

Let us solve for n.

$1$

$1$

$1\cdot \frac{16}{3}$

$5.333$

$n>5.333$

We can also write next terms of our sequence as:

$\frac{3}{16},\frac{6}{16}, \frac{9}{16},\frac{12}{16},\frac{15}{16},\frac{18}{16}$

Therefore, Vicki will run more than 1 mile when she is jogging for 6th time.