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Answer :
The algebraic expression for the sequence is aₙ = 35.6 + 2n
The 8th and 65th term for this pattern are 51.6 and 165.6 respectively.
The term number that has a term value of 109.6 is the 37th term (n = 37)
What is the algebraic expression for the sequence?
An arithmetic progression (AP) is a sequence of numbers where each term is obtained by adding a fixed constant value to the previous term. This constant value is called the common difference, denoted by d. The general formula for the nth term of an arithmetic progression is:
aₙ = a₁ + (n-1)d
where aₙ is the nth term of the sequence, a₁ is the first term, n is the position of the term in the sequence, and d is the common difference.
From the given information, a₁ = 37.6, d = 39.6 - 37.6 = 2
The algebraic expression for the sequence will be:
aₙ = a₁ + (n-1)d
aₙ = 37.6 + (n-1)2
aₙ = 37.6 + 2n - 2
aₙ = 35.6 + 2n
The 8th and 65th term for this pattern will be:
For 8th term, n = 8:
aₙ = 35.6 + 2n
aₙ = 35.6 + 2(8) = 51.6
For 65th term, n = 65:
aₙ = 35.6 + 2n
aₙ = 35.6 + 2(65) = 165.6
The term number that has a term value of 109.6 will be:
aₙ = 109.6
aₙ = 35.6 + 2n
109.6 = 35.6 + 2n
2n = 109.6 - 35.6
2n = 74
n = 74/2
n = 37
Learn more about arithmetic progression on:
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