Question

B. What are the second and third terms of this arithmetic sequence? 80, 페, 페, 125,...........

Answer 1

The 2nd and 3rd term of an AP is found to be (a₂ = 95) and (a₃ = 110).

What is the sequence of AP arithmetic progression?

In Arithmetic Progression, the difference between the two numerical orders is a fixed number (AP). Arithmetic Sequence is another name for it.

We'd come across a few key concepts in AP that had been labeled as:

• The first term (a)
• Common difference (d)
• Term nth (an)
• The total of first n terms (Sn)

As shown below, the AP can also be referred to in terms of common differences.

• The following is the procedure for evaluating an AP's n-th term:  an = a + (n − 1) × d
• The arithmetic progression sum is as follows: Sn = n/2[2a + (n − 1) × d].
• Common difference 'd' of an AP: d = a2 - a1 = a3 - a2 = a4 - a3 = ......      = an - an-1.

Now, the given sequence is; 80, _, _, 125.

The series comprises of four given terms.

Let the first term be 'a₁' = 180.

The second term be 'a₂'.

The third term be 'a₃'.

And, the fourth term is 'a₄' = 125.

Use the nth term formula to find the common difference 'd'.

n-th term:  an = a + (n − 1) × d

a₄ = a + (n - 1)d

125 = 80 + (4 - 1)d

45 = 3d

d = 15

Thus, the common difference is 15.

The second term is calculated as;

a₂ = a₁ + d

a₂ = 80 + 15

a₂ = 95.

The third term is estimated as;

a₃ = a₂ + d

a₃ = 95 = 15

a₃ = 110

Therefore, the 2nd and third term of an AP is computed as 95 and 110.

To know more about Arithmetic Sequence, here

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