Respuesta :

The missing terms of the given arithmetic sequence AP are 14, 21, 28, 35.

What exactly is arithmetic progression?

An arithmetic progression (AP) is a sequence with the same distinctions between each successive term.

  • Each term (apart from the first) in an arithmetic progression is derived by adding a specific number to the term before the first one.
  • For the initial term 'a' of an AP as well as the common difference 'd,' the very next arithmetic progression equations are frequently used to solve different AP problems.
  • An AP's most common difference 'd': d = a2 - a1 = a3 - a2 = a4 - a3 =...... = a - an-1.
  • nth term of an AP: an = a + (n - 1) d
  • The sum of an AP's n terms is: Sn = n/2(2a+(n-1)d) = n/2(a + l), where l is the AP's final term.

Now, in response to the question;

The arithmetic sequence.14,..., 28, ............

There are total 4 terms in the series.

Let the initial term is  'a₁' is given as 14.

Let the second term is 'a₂'.

Let the third term be 'a₃' which is given as 28.

Ans, the let the fourth term is represented as 'a₄'.

As, we know that in the AP, the difference of the two consecutive terms is equal and called as common difference.

Thus,

d = a₂ - a₁      ........(equation 1)

d = a₃ - a₂     .......(equation 2)

Thus, equating the two equation;

a₂ - a₁ = a₃ - a₂

Substituting the values;

a₂ - 14 = 28 - a₂

Simplifying the equation;

2a₂ = 28 + 14

2a₂ = 42

a₂ = 21.

Put the obtained value in equation 1 and find d.

d = a₂ - a₁

d = 21 - 14

d = 7

Now, estimate a₄.

a₄ = a₃ + d

a₄ = 28 + 7

a₄ = 35

Therefore, the complete arithmetic sequence is 14, 21, 28, 35.

To know more about the arithmetic sequence, here

https://brainly.com/question/6561461

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