How many terms are there In an arithmetic Sequence with a common different of 4 and with the first and last term 3 and 59 Respectively.

Let Common difference = d =4

First term= a -3
Last term = l = 59
And number of terms = n

l=a+(n-1)d
59= 3 + (n-1)4
59=3+4n-4
59=4n-1
60=4n
60/4 =n
15=n

#There are 15 terms in the sequence

Well, let's see. The first term is 3, and the last term is 59. We know that the common difference is 4. To find the number of terms, we can use the formula:

n = (last term - first term + common difference) / common difference

So, plugging in the values, we get:

n = (59 - 3 + 4) / 4

Simplifying, we get:

n = 60/4

And that equals:

n = 15

So, there are 15 terms in this arithmetic sequence. That's a lot of terms! Hopefully, they didn't get too tired counting them all.

To find the number of terms in an arithmetic sequence, we can use the formula:

n = (last term - first term) / common difference + 1

Given:
First term (a₁) = 3
Last term (aₙ) = 59
Common difference (d) = 4

We can substitute these values into the formula:

n = (59 - 3) / 4 + 1
n = 56 / 4 + 1
n = 14 + 1
n = 15

Therefore, there are 15 terms in the arithmetic sequence.

To find the number of terms in an arithmetic sequence, we need to use the formula for the nth term of an arithmetic sequence.

The formula for the nth term of an arithmetic sequence is:

an = a1 + (n - 1)d

Where:
an = nth term
a1 = first term
d = common difference
n = number of terms

Given that the first term (a1) is 3, the last term is 59, and the common difference (d) is 4, we can substitute these values into the formula:

59 = 3 + (n - 1) * 4

To simplify the equation, we distribute 4 to (n - 1):

59 = 3 + 4n - 4

Combine like terms:

59 + 1 = 4n

60 = 4n

Divide both sides of the equation by 4 to isolate n:

n = 60/4

Simplifying further, we have:

n = 15

Therefore, there are 15 terms in the arithmetic sequence.