write the explicit formula for the sequence 7,2,-3,-8,-13 and find a 14

To find the explicit formula for the given sequence, we observe that each term is decreasing by 5.

We can define the nth term of the sequence using the formula:

aₙ = a₁ + (n-1)d

where aₙ represents the nth term, a₁ is the first term, n is the position of the term, and d is the common difference.

In this case, the first term (a₁) is 7, and the common difference (d) is -5 (since each term is decreasing by 5).

Using the formula, we can find the nth term of the sequence:

aₙ = 7 + (n-1)(-5)

Now, let's find the 14th term (a₁₄):

a₁₄ = 7 + (14-1)(-5)
= 7 + (13)(-5)
= 7 - 65
= -58

Therefore, the explicit formula for the given sequence is aₙ = 7 + (n-1)(-5), and the 14th term of the sequence is -58.

To find the explicit formula for the given sequence, we need to identify the pattern in the numbers. Looking at the sequence, we can observe that each number is obtained by subtracting 5 from the previous number.

Therefore, the explicit formula for this sequence can be written as:

nₙ = a + (n - 1)d

Where:
nₙ is the nth term in the sequence
a is the first term in the sequence
d is the common difference (in this case, it is -5)
n is the position of the term in the sequence

Now, let's substitute the values:
a = 7 (the first term)
d = -5 (the common difference)

So, the explicit formula for the sequence is:
nₙ = 7 - 5(n - 1)

To find the 14th term of the sequence, we substitute n = 14 into the formula:

n₁₄ = 7 - 5(14 - 1)
n₁₄ = 7 - 5(13)
n₁₄ = 7 - 65
n₁₄ = -58

Therefore, the 14th term of the sequence is -58.

You have posted this before. Read my previous answer.