Question

Firewood is stacked in a pile. The bottom row has 20 logs, and the top row was 14 logs. Each row has one more log than the row above it. How many logs are in the pile?

Answer 1

Answer:

119 logs.

Step-by-step explanation:

We can see that logs in rows of firewood pile are in arithmetic sequence. First term of our sequence is 14 and every successive term is 1 more than previous term.

We will use $n=\frac{\text{Last term - first term}}{\text{common difference}} +1$ to find numbers of terms of our sequence.

$n=\frac{20-14}{1} +1=6+1=7$

We will use  sum formula of arithmetic series to solve our problem.

$S_n=\frac{(a_1+a_n)}{2} *n$, where $a_1$ is first term of sequence, $a_n$ is last term of sequence and n is number of terms in the sequence.

Upon substituting our given values we will get,

$\text{Number of logs in the pile}=\frac{14+20}{2}*7$

$\text{Number of logs in the pile}=\frac{34}{2}*7$

$\text{Number of logs in the pile}=17*7=119$

Therefore, there are 119 logs in the pile.

Answer 2

Since, each row has one more log than the row above it

so, this is arithematic sequence

We are given that

First row is

$=14$

so,

$a_1=14$

Last row is

$=20$

so,

$a_n=14$

Each row has one more log than the row above it

so,

$d=1$

now, we can find number of rows

$a_n=a_1+(n-1)d$

we can plug values

$20=14+(n-1)1$

we can solve for n

$6=(n-1)1$

$n=7$

now, we can find total number of logs

$S=\frac{n(a_1+a_n)}{2}$

now, we can plug values

$S=\frac{7(14+20)}{2}$

$S=\frac{7(14+20)}{2}$

$S=119$

So,

Number of logs in the pile are 119........Answer