Answer:
Arithmetic Sequence:
An Arithmetic sequence is a series of number in order where the difference between one term and the next is a constant.
It follows the rule below:
Xₙ = a + d(n-1)
Where;
a = is the first term
d = common difference
Arithmetic Mean
It is the average value among a set of numbers
It is given by the formula:
Mean = ∑¹ₙ[tex]\frac{Xi + Xn}{n}[/tex]
where;
x = the sequence of terms
n = the number of terms
To solve the given problem,
Given:
Mean = 39
X₂ = 32
n = 2 → number of terms
Required:
X₁ = First term
Solution:
Using Arithmetic Mean:
Mean = [tex]\frac{Xi + Xn}{n}[/tex]
39 = [tex]\frac{X1 + 32}{2}[/tex]
2(39) = X₁+32
78 = X₁ + 32
X₁ = 78 - 32
X₁ = 46
Checking
39 = [tex]\frac{46 + 32}{2}[/tex]
39 = 39
Thus , the other term is 46
Using Arithmetic Sequence:
Xₙ = a + d(n-1)
d = 39 - 32 considering the first and second term as we have three term if using arithmetic sequence. 32, 39, X₃
= 32 + (7)
(3-1)
=32 + (7)
(2)
= 32 + 14
X₃ = 46
For more information about arithmetic sequence visit the below link:
https://brainly.ph/question/554855
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