Answer:
a₄₅ = 13
Step-by-step explanation:
The n-th term of an arithmetic sequence with first term a₁ and common difference d is given by the formula ...
aₙ = a₁ +d(n -1)
You want the 45th term where a₁ = 2 and d = 1/4. Putting these values into the formula gives ...
a₄₅ = a₁ +d(n -1) = 2 +(1/4)(45 -1)
Evaluating this expression, we have ...
a₄₅ = 2 +44/4 = 2 +11
a₄₅ = 13
The 45th term of the sequence is 13.
The forty-fifth term of the sequence whose initial term a = [tex]2[/tex] and common difference d = [tex]\frac{1}{4}[/tex] is [tex]13[/tex]
How to find the nth term of the Arithmetic series?
The nth term of the arithmetic series is find by [tex]Tn = a+(n-1)d[/tex] where Tn is the nth term of the series a is called the initial number and is the common difference between two number. n is the number of term of that arithmetic series.
In the given series initial term a = [tex]2[/tex] and common difference d = [tex]\frac{1}{4}[/tex]
We have the find the forty-fifth term of the given series.
= [tex]Tn=a+(n-1)d[/tex]
= [tex]Tn = 2+(45-1)\frac{1}{4}[/tex]
= [tex]Tn=2+44\cdot\frac{1}{4}[/tex]
= [tex]Tn = 2+11[/tex]
= [tex]Tn = 13[/tex]
So, the forty-fifth term of the sequence whose initial term a = [tex]2[/tex] and common difference d = [tex]\frac{1}{4}[/tex] is [tex]13[/tex]
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