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Answer:

[tex]A_{38} = 350[/tex]

Step-by-step explanation:

The 5th term of the arithmetic sequence is 53. We can write the equation:

[tex]a + 4d = 53...(1)[/tex]

The 6th term of the arithmetic sequence is 62. We can write the equation:

[tex]a + 5d = 62...(2)[/tex]

Subtract the first equation from the second one to get:

[tex]5d - 4d = 62 - 53[/tex]

[tex]d = 9[/tex]

The first term is

[tex]a + 4(9) = 53[/tex]

[tex]a + 36 = 53[/tex]

[tex]a = 53 - 36[/tex]

[tex]a = 17[/tex]

The 38th term of the sequence is given by:

[tex] A_{38} = a + 37d[/tex]

[tex]A_{38} = 17+ 37(9)[/tex]

[tex]A_{38} = 350[/tex]

Answer:

[tex]A_{38}=386[/tex]

Step-by-step explanation:

We have been given an arithmetic sequence gas [tex]A_1,A_2,A_3,A_4[/tex] as :53,62,71,80. We are asked to find [tex]A _{38}[/tex].

We know that an arithmetic sequence is in format [tex]a_n=a_1+(n-1)d[/tex], where,

[tex]a_n[/tex] = nth term,

[tex]a_1[/tex] = 1st term of sequence,

n = Number of terms,

d = Common difference.

We have been given that 1st term of our given sequence is 53.

Now, we will find d by subtracting 71 from 80 as:

[tex]d=80-71=9[/tex]

[tex]A_{38}=53+(38-1)9[/tex]

[tex]A_{38}=53+(37)9[/tex]

[tex]A_{38}=53+333[/tex]

[tex]A_{38}=386[/tex]

Therefore, [tex]A_{38}=386[/tex].

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