jasonwright
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the third term of an arithmetic sequence is 24 and the fifth is 32 if the first term is a1. which is an equation nth term of the sequence

Respuesta :

bcalle
an = a1 + (n - 1)(d)
Where a1 is the first term and d is the common difference.
First find d, the common difference.
24, ____, 32
a3 a4 a5
Subtract 32-24 = 8
Subtract a5 - a3 = 2
Divide 8/2 = 4
d = 4
Use d and one of the values they give us to find a1.
a3 = 24
24 = a1 + (3 - 1)(4)
24 = a1 + 2(4)
24 = a1 + 8
Subtract 8 from both sides
16 = a1
an = 16 + (n - 1)(4)
Can also be written
an = 16 + 4n - 4
an = 4n + 12
isyllus

Answer:

The nth term of the sequence is [tex]a_n=4n+12[/tex]

Step-by-step explanation:

Given: [tex]a_3=24,\ \ a_5=32[/tex]

First term: [tex]a_1[/tex]

Formula:

[tex]a_n=a_1+(n-1)d[/tex]

where, d is common difference

[tex]a_3=24[/tex]

[tex]a_1+2d=24[/tex]

[tex]a_1+4d=32[/tex]

Subtract both equation

[tex]2d=32-24[/tex]

[tex]2d=8[/tex]

[tex]d=4[/tex]

Put d=4 into [tex]a_1+2d=24[/tex]

[tex]a_1+2(4)=24[/tex]

[tex]a_1=16[/tex]

Now, we will find nth term of the sequence.

[tex]a_n=16+(n-1)4[/tex]

[tex]a_n=16+4n-4[/tex]

[tex]a_n=4n+12[/tex]

Hence, The nth term of the sequence is [tex]a_n=4n+12[/tex]

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