Question

Find the 2nd and 3rd term of the sequence -1, ____, _____, 56, 75

Answer 1

To find the 2nd and 3rd terms of the sequence -1, ____, ____, 56, 75, let’s first identify the pattern.

We have the terms:
- 1st term: -1
- 4th term: 56
- 5th term: 75

We can first find the difference between the 4th and 5th terms:

\[ 75 - 56 = 19 \]

This tells us that the sequence increases by 19 between the 4th and 5th terms.

Next, we can look for a pattern in the terms. We will check the difference between the 3rd and 4th terms:

Let’s denote:
- 2nd term as \( a_2 \)
- 3rd term as \( a_3 \)

We know:
- \( a_4 = 56 \)
- \( a_5 = 75 \)

Now let's calculate \( a_3 \):
Assume there’s a constant difference \( d \) between consecutive terms. We know the difference from the 4th term to the 5th term is 19.

Now, let’s work backwards:
\[ a_4 - a_3 = d \]
\[ a_3 - a_2 = d \]
\[ a_2 - (-1) = d \]

Let’s start calculating from \( a_4 \) to \( a_3 \):
Assuming \( a_3 = 56 - d \) and \( d = 19 \),
\[ a_3 = 56 - 19 = 37 \]

Now calculate \( a_2 \):
\[ a_2 = a_3 - d = 37 - 19 = 18 \]

So the sequence is:
- 1st term: -1
- 2nd term: 18
- 3rd term: 37
- 4th term: 56
- 5th term: 75

Thus, the 2nd and 3rd terms of the sequence are **18** and **37**, respectively.