The sum of the sequence $2 + 3 + 4 + \dots + 91$ is an arithmetic series, where:

• The first term ($a_1$) is 2,
• The last term ($a_n$) is 91,
• The common difference ($d$) is 1.

To find the sum of this arithmetic series, we use the formula for the sum of an arithmetic series:

$S_n = \frac{n}{2} \times (a_1 + a_n)$

Where:

• $n$ is the number of terms,
• $a_1$ is the first term,
• $a_n$ is the last term.

Step 1: Find the number of terms ($n$)

To determine $n$, we use the formula for the $n$-th term of an arithmetic series:

$a_n = a_1 + (n - 1) \times d$

Substitute the values we know:

$91 = 2 + (n - 1) \times 1$ $91 = 2 + n - 1$ $91 = n + 1$ $n = 90$

Step 2: Calculate the sum

Now, using the sum formula:

$S_n = \frac{90}{2} \times (2 + 91)$ $S_n = 45 \times 93$ $S_n = 4185$

Thus, the sum of the series is 4185.

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Would you like further details or have any other questions on this?

Here are some related questions:

1. How do you calculate the sum of an arithmetic series with different terms?
2. How can you find the sum of a geometric series?
3. How does changing the common difference affect the sum of an arithmetic series?
4. What is the formula for the sum of the first $n$ natural numbers?
5. How do you calculate the sum of squares or cubes of numbers in a sequence?

Tip: Always check if the series is arithmetic before applying the sum formula!