To find a(1), simply look at the first term, which is -17. This gives a starting point for the recursive formula.
Then, we want to write the recursive formula as a(n) = a(n - 1) + c, where c is the number you add to a term to get the next term. You can see from the values given that you are adding 9 to each term to get the next one, so the recursive formula would be a(n) = a(n - 1) + 9.
First term of sequence of arithmetic (a₁) is -17 and aₙ is -17 + 9(n-1)
What is arithmetic sequence?
A arithmetic sequence is defined as an arrangement of numbers which is particular order.
The formula to find the general term of an arithmetic sequence is,
aₙ = a₁ + (n-1)d
The geometric sequence defined as a series represents the sum of the terms in a finite or infinite geometric sequence. The successive terms in this series share a common ratio.
The nth term of a geometric progression is expressed as
Tₙ = arⁿ⁻¹
Given data :
The arithmetic sequence -17, -8, 1, 10,...
First term of sequence of arithmetic (a₁) = -17
The common difference of arithmetic (d) = difference between the two term
The common difference of arithmetic (d) = -8 - (-17)
The common difference of arithmetic (d) = -8 + 17
The common difference of arithmetic (d) = 9
To determine the n term of arithmetic sequence
The nth term of a arithmetic sequence is expressed as :
aₙ = a₁ + (n-1)d
substitute the values of a₁ and d in the formula,
aₙ = -17 + (n-1)9
Let n = 5
a₅ = -17 + (5 - 1)9
a₅ = -17 + (4)9
a₅ = -17 + 45
a₅ = 28
Learn more about arithmetic sequence here :
brainly.com/question/21961097
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