Question

What is the explicit formula for the arithmetic sequence in the table below? n 1 2 3 4 5 an 9.2 7.4 5.6 3.8 2

Answer 1

commin difference  d = 7.4 - 9.2 = -1.8  and first term a1 = 1   so the explicit formula is  

an = 9.2 +(n - 1)*-1.8   

an =  9.2 - 1.8(n - 1)

Answer 2

The explicit formula for the arithmetic sequence is $\rm a_n = 9.2 -1.8(n-1)$.

We have to determine

What is the explicit formula for the arithmetic sequence?

What is the general formula of an arithmetic sequence?

The general formula of the arithmetic sequence is;

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

Where $\rm a_n$ is the nth term of the sequence, d is a common difference, n is the number of terms.

Firstly find the common difference between the terms.

$\rm d = 7.4 - 9.2\\\\ d = -1.8$

Substitute all the values in the formula;

$\rm a_n = a_1+d(n-1)\\\\ a_n = 9.2+(-1.8)(n-1)\\\\a_n = 9.2 -1.8(n-1)$

Hence, the explicit formula for the arithmetic sequence is $\rm a_n = 9.2 -1.8(n-1)$.

To know more about the Arithmetic sequence click the link given below.

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