×

## Arithmetic Progressions

What's the sum of the first 100 positive integers? How about the first 1000? Learn the fun and fast way to solve problems like this. See more

# Problem Solving

Non-zero numbers $$a, b, c, d, e$$ form an arithmetic progression. If $\frac{b+d}{2} + \frac{a+e}{4} = kc,$ find the value of $$k$$.

Two sequences $$\{ x, a_1, a_2, a_3, y \}$$ and $$\{ x, b_1, b_2, b_3, b_4, b_5, y \}$$ each form an arithmetic progression. If $$x \neq y$$, what is the value of

$\frac{a_2 - a_1}{b_5 - b_4} ?$

For an arithmetic progression $$\{a_n\}$$, the following equalities hold: $a_3 + a_5 = 36, \quad a_2 a_4 = 180.$

Find the largest $$n$$ such that $$a_n < 100.$$

An arithmetic progression $$\{a_n \}$$ satisfies $a_2 + a_4 + a_6 + \cdots + a_{2n} = 2n^2 + 3n.$ Find the value of $a_3 + a_6 + a_9 + \cdots + a_{18}.$

For an arithmetic progression $$\{ a_n \}$$, $$a_3 = 8$$ and $$a_{10} = 29$$. If $$a_n = 200$$, what is $$n ?$$

×