Given the Arithmetic sequence A1,A2,A3,A4 53, 62, 71, 80 What is the value of A38?
Accepted Solution
A:
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]