Respuesta :
The given pattern 5/7, 8/7, 11/7, 2, ....... is in the form of the arithmetic progression AP. The next 3 terms are 17/7, 20/7, 23/7.
What is defined as the arithmetic progression AP?
An arithmetic progression is a sequence whose terms continue to increase and otherwise decrease by a constant number. The common difference is the set amount through which they either increase or decrease.
The following arithmetic progression formulas are frequently utilized to solve various AP problems for the initial term 'a' of an AP and the common difference 'd'-
- Common difference 'd' = a₂ - a₁ = a₃ - a₂ = a₄ - a₃ = ....= an - a(n-1).
- nth term : an = a + (n - 1) d
- Sum of nth terms; Sn = n/2(2a+(n-1)d) = n/2(a + l), where 'l' is the last term of an AP.
Now, as per the stated question;
The AP given as; 5/7, 8/7, 11/7, 2, ...........
The series consists of four given terms.
Consider the initial term be 'a₁' = 5/7.
Then, the second term be 'a₂' = 8/7.
And, the third term be 'a₃' = 11/7.
And, the fourth term is 'a₄' = 2.
The AP have the same common difference. so,
d = a₃ - a₂
Substitute the values.
d = 11/7 - 8/7
d = 3/7
Thus, the common difference is 3/7.
or d = a₄ - a₃ (Put the values)
d = 2 - 11/7
d = 3/7
As, a₃ - a₂ = a₄ - a₃
Thus, we can conclude that the given sequence is in AP.
The fifth term will be; a₅ = a₄ + d = 2 + 3/7
a₅ = 17/7
Now, the 6th term will be; a₆ = a₅ + d = 17/7 + 3/7
a₆ = 20/7
Similarly, the 7th term will be; a₇ = a₆ + d = 20/7 + 3/7
a₇ = 23/7
Therefore, it can be said that the given sequence is in AP next three terms be 17/7, 20/7, 23/7.
To know more about the arithmetic progression, here
https://brainly.com/question/24989563
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