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The arithmetic mean between two terms in an arithmetic sequences is 39. if one of these terms is 32, find the other term. w/ solution plss help...

Sagot :

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

X = 46

For more information about arithmetic sequence visit the below link:

https://brainly.ph/question/554855

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