Lesson

# 1.3 SEQUENCES AND SERIES

After completing this section, you should be able to:

• understand what sequence is: $4,9,14,19, \cdots$
• determine terms of series using general term: $u_n = 4n+2$
• find terms of arithmetic sequences: $3,5,7,9, \cdots$
• solve application problems involving arithmetic sequences
• find terms of geometric sequences: $1, 2, 4, 8, \cdots$
• solve application problems involving geometric sequences
• solve practical applications involving compound interest
• write series in sigma notation: $\displaystyle \sum_{n=1}^{10}{A_n}$
• determine the sum of arithmetic sequences:
• $S_n = \displaystyle \dfrac{n}{2}(u_1 + \ell)$
• $S_n = \displaystyle \dfrac{n}{2}\Big[2u_1 + (n-1)d\Big]$
• determine the sum of geometric sequences:
• $S_n = \displaystyle \dfrac{u_1(r^n – 1)}{r-1}$
• $S_n = \displaystyle \dfrac{u_1(1 – r^n)}{1 – r}$
• determine the sum of infinite series, so called sum to infinity: $S_{\infty} = \displaystyle \dfrac{u_1}{1-r}$