9. Sequences, Series, & Induction

Find the sum of the first 20 terms of the arithmetic sequence: 4, 10, 16, 22,……….

Find the sum of the first 50 terms of the arithmetic sequence: -10, -6, -2, 2,....

Find 1+2+3+4+...+ 100, the sum of the first 100 natural numbers.

Find the sum of the first 60 positive even integers.

Find the sum of the even integers between 21 and 45.

Find the sum of the odd integers between 30 and 54.

Write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.

${\sum }_{i=1}^{17}(5i+3)$

Write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.

${\sum }_{i=1}^{30}(-3i+5)$

Write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.

${\sum }_{i=1}^{100}4i$

Use the graphs of the arithmetic sequences {a} and {b} to solve Exercises 51-58.

Find a₁₄+b₁₂.

Use the graphs of the arithmetic sequences {a} and {b} to solve Exercises 51-58. If {a_n} is a finite sequence whose last term is -83, how many terms does {a_n} contain?

Use the graphs of the arithmetic sequences {a} and {b} to solve Exercises 51-58. Find the difference between the sum of the first 14 terms of {b_n} and the sum of the first 14 terms of {a_n}.

In the sequence 21,700, 23,172, 24,644, 26,116,... which term is 314,628?

Show that the sum of the first n positive odd integers,1 +3 +5 + ··· + (2n − 1), ... is n².

Use the formula $a_n=4+(n-1)(-7)$ to find the eighth term of the sequence $4,-3,-10,\dots$