Kye

2021-08-12

Find the 72nd term or the arithmetic sequence -27, -11, 5,

aprovard

Step 1
first term $\left(a\right)=-27$
common difference $\left(d\right)=-11-\left(-27\right)=5-\left(-11\right)$
common difference $\left(d\right)=16$
Step 2
n-th term of arithmatic sequence=
${T}_{n}=a+\left(n-1\right)d$
$a=-27,d=16,n=72$
${T}_{72}=-27+\left(72-1\right)16$
${T}_{72}=-27+1136$
${T}_{72}=1109$

Jeffrey Jordon

Answer is given below (on video)

Jazz Frenia

To find the 72nd term of an arithmetic sequence, we need to determine the formula for the nth term of the sequence. The formula for an arithmetic sequence is given by:
${a}_{n}={a}_{1}+\left(n-1\right)·d$ where ${a}_{n}$ represents the nth term of the sequence, ${a}_{1}$ is the first term, $n$ is the term number, and $d$ is the common difference between consecutive terms.
In this case, we are given the first three terms of the sequence: -27, -11, and 5. Let's use these values to find the common difference ($d$).
We can observe that to move from the first term (-27) to the second term (-11), we add 16. Similarly, to move from the second term (-11) to the third term (5), we add 16. Hence, the common difference between consecutive terms is 16.
Now, we can substitute the values into the formula to find the 72nd term. In this case, ${a}_{1}=-27$, $n=72$, and $d=16$.
${a}_{72}=-27+\left(72-1\right)·16$
Let's calculate the value:
${a}_{72}=-27+71·16$
To simplify the calculation, let's break it down into smaller steps. First, we'll find $71·16$.
$71·16=1136$
Now, we can substitute this value back into the equation to find the 72nd term:
${a}_{72}=-27+1136$
Simplifying further:
${a}_{72}=1109$
Therefore, the 72nd term of the arithmetic sequence -27, -11, 5 is 1109.

Andre BalkonE

Result:
$1109$
Solution:
Given:
${a}_{n}={a}_{1}+\left(n-1\right)d$
In this case, the first term is ${a}_{1}=-27$ and the common difference is $d=-11-\left(-27\right)=16$.
Substituting these values into the formula, we get:
${a}_{72}=-27+\left(72-1\right)\left(16\right)$
Simplifying the expression:
${a}_{72}=-27+71\left(16\right)$
Now we can calculate the value:
${a}_{72}=-27+1136=1109$
Therefore, the 72nd term of the arithmetic sequence is $1109$.

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