Problem 47

Question

Find the sum of the first 10 terms of the arithmetic sequence with first term 14 and last term 68 .

Step-by-Step Solution

Verified

Answer

The sum of the first 10 terms of the given arithmetic sequence is 410.

1Step 1: Identify the given values

We are given the following: - First term ($a_1$) = 14 - Last term ($a_{10}$) = 68 - Number of terms (n) = 10

2Step 2: Use the arithmetic series formula

Using the arithmetic series formula, we can find the sum of the first 10 terms ($S_{10}$): $S_{10} = \frac{n(a_1 + a_{10})}{2}$ Plugging in the given values:

3Step 3: Plug the given values into the formula

$S_{10} = \frac{10(14 + 68)}{2}$

4Step 4: Simplify and solve for the sum of the first 10 terms

Now, we can simplify the expression and find the sum: $S_{10} = \frac{10(82)}{2}$ $S_{10} = \frac{820}{2}$ $S_{10} = 410$

5Step 5: State the answer

The sum of the first 10 terms of the given arithmetic sequence is 410.

Problem 47

Problem 48

Other exercises in this chapter

Problem 47

A company's advertising budget is currently $\$ 500,000$ per year. For the next several years, they will cut the budget by $10 \%$ per year. a) Find the gen

View solution

Problem 47

Evaluate each series. $$\sum_{i=1}^{5}(-1)^{i+1} \cdot(i)$$

View solution

Problem 48

Use the binomial theorem to expand each expression. $$\left(\frac{1}{3} a+2 b\right)^{5}$$

View solution

Problem 48

In January $2008,$ approximately 1000 customers at a grocery store used the self-checkout lane. The owners predict that number will increase by $20 \%$ per

View solution