Find the Sum of the Arithmetic Series 7 + 10 + 13 +...+ 157

TL;DR

Calculate the sum of an arithmetic sequence by finding the missing term and applying the formula.

Transcript

in this problem we're being asked to find this sum so the trick is to realize that if we think of this as a sequence this is an arithmetic sequence so an arithmetic sequence is one in which each term except the first is obtained by adding a number over and over again so we're going to use the formula for the nth term of an arithmetic sequence and w... Read More

Key Insights

• 🍹 Understanding the concept of arithmetic sequences is essential to solving problems involving sum calculations.
• 🍉 The formula for the nth term of an arithmetic sequence aids in finding missing terms within a sequence.
• 🍹 Calculating the sum of an arithmetic sequence involves determining the missing term and applying the sum formula.

Questions & Answers

Q: How is an arithmetic sequence defined, and what makes it different from other sequences?

An arithmetic sequence is characterized by a common difference between consecutive terms. Each term is obtained by adding the same number to the previous term, distinguishing it from other types of sequences like geometric sequences or Fibonacci sequences.

Q: What formula is used to find the nth term of an arithmetic sequence, and how is it applied in this problem?

The formula for the nth term of an arithmetic sequence is a_n = a_1 + (n-1)d, where a_n is the nth term, a_1 is the first term, n is the term number, and d is the common difference. In the problem, this formula helps determine the missing term of the sequence.

Q: How is the missing term of the arithmetic sequence found in the problem?

By substituting the known values (a_1=7, a_n=157, d=3) into the nth term formula and solving for n, the missing term is calculated to be 51.

Q: How is the sum of the arithmetic sequence calculated once the missing term is found?

The sum of the first n terms of an arithmetic sequence is found using the formula S_n = n/2(a_1 + a_n). By plugging in the values for n=51, a_1=7, and a_n=157, the sum is evaluated to be 4182.

Summary & Key Takeaways

• The problem involves finding the sum of an arithmetic sequence by determining the missing term.

• Using the formula for the nth term of an arithmetic sequence, the missing term is calculated to be 51.

• Plugging the values into the sum formula gives a final sum of 4182 for the arithmetic sequence.