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

Question

aprovard · Accepted Answer

Step 1   first term (a)=−27  common difference (d)=−11−(−27)=5−(−11)  common difference (d)=16  Step 2  n-th term of arithmatic sequence=  Tn=a+(n−1)d  a=−27,d=16,n=72  T72=−27+(72−1)16  T72=−27+1136  T72=1109

Jeffrey Jordon · Accepted Answer

Answer is given below (on video)

Jazz Frenia · Accepted Answer

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} + (n - 1) \cdot 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 + (72 - 1) \cdot 16

Let's calculate the value:

a_{72} = - 27 + 71 \cdot 16

To simplify the calculation, let's break it down into smaller steps. First, we'll find

71 \cdot 16

.

71 \cdot 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 · Accepted Answer

Result:1109Solution:Given:an=a1+(n−1)dIn this case, the first term is a1=−27 and the common difference is d=−11−(−27)=16.Substituting these values into the formula, we get:a72=−27+(72−1)(16)Simplifying the expression:a72=−27+71(16)Now we can calculate the value:a72=−27+1136=1109Therefore, the 72nd term of the arithmetic sequence is 1109.

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

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