The 2nd and 3rd term of an AP is found to be (a₂ = 95) and (a₃ = 110).
<h3>What is the sequence of AP arithmetic progression?</h3>
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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