Respuesta :
Answer:
424
Step-by-step explanation:
Since the difference between consecutive terms are constant, that is
19 - 14 = 14 - 9 = 9 - 4 = 5 ← common difference (d)
Then these are the terms of an arithmetic sequence with n th term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term = 4 and d the common difference, hence
[tex]a_{85}[/tex] = 4 + (84 × 5) = 4 + 420 = 424
The required 85th term of the arithmetic progression is 424
A series 4,9,14,19, is given the 85th term of the given arithmetic progression is to be determined.
What is arithmetic progression?
Arithmetic progression is the series of numbers that have common differences between adjacent values.
What is geometric progression?
Geometric progression is a sequence of series whose ratio with adjacent values remains the same.
for given series, 4,9,14,19,
First term ( a ) = 4 and Common difference ( d ) = 9-4 = 5
Now the nth term of the arithmetic progression is
[tex]a_n = a_1 + (n-1)d[/tex]
a85th = 4 + (85 - 1 )5
= 4 + 84 * 5
= 424
Thus, the required 85th term of the arithmetic progression is 424
Learn more about arithmetic progression here: https://brainly.com/question/20334860
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