Respuesta :
The 15th term of the arithmetic sequence will be 75. so option C is correct.
What is arithmetic sequence?
An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.
We have Given an arithmetic sequence with a7=19 and a12=54.
Its nth term is
T_n = a + (n-1)d
So,
[tex]19 = a + (7-1)d\\\\\\ 54= a + (12-1)d[/tex]
(for all positive integer values of n)
Simplifying;
19 = a + 6d
54 = a +11d
Solving;
5d = 35
d = 7
Also, 19 = a + 6d
a = 19 - 42 = -23
To find the 15 th term;
a(15) = a + (15 -1)7
a(15) = - 23 + 98
a(15) = 75
Hence the 15th term of the arithmetic sequence will be 75. so option C is correct.
Learn more about arithmetic sequence here:
https://brainly.com/question/3702506
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