A _______________________ expresses each new term of a sequence based on the preceding term in the sequence.

• recursive formula

• explicit formula

A ___________________________ is a formula used to calculate the nth term of a sequence using the term's position (or term number) in the sequence.

• recursive formula

• explicit formula

Select the following below: recursive formula for geometric sequence

• $g_{n\ }=\ g_{n-1}\cdot r$

• $g_n\ =\ g_1\cdot r^{n-1}$

• $a_n\ =\ a_{n-1}+d$

• $a_n=a_1+d\left(n-1\right)$

Select the following below: explicit formula for arithmetic sequence

• $g_{n\ }=\ g_{n-1}\cdot r$

• $g_n\ =\ g_1\cdot r^{n-1}$

• $a_n\ =\ a_{n-1}+d$

• $a_n=a_1+d\left(n-1\right)$

Select the following below: explicit formula for geometric sequence

• $g_{n\ }=\ g_{n-1}\cdot r$

• $g_n\ =\ g_1\cdot r^{n-1}$

• $a_n\ =\ a_{n-1}+d$

• $a_n=a_1+d\left(n-1\right)$

Select the following below: recursive formula for arithmetic sequence

• $g_{n\ }=\ g_{n-1}\cdot r$

• $g_n\ =\ g_1\cdot r^{n-1}$

• $a_n\ =\ a_{n-1}+d$

• $a_n=a_1+d\left(n-1\right)$

Write a recursive formula for the arithmetic sequence:

2, 5, 8, 11, ...

•  $g_n=g_{n-1}\cdot3$ 

• $a_n=2+3\left(n-1\right)$

• $g_n=2\cdot3^{n-1}$

•  $a_n=a_{n-1}+3$ 

Tags

CCSS.HSF.BF.A.2

Write a recursive formula for the geometric sequence:

1, -4, 16, -64, ...

• $a_n=a_{n-1}-5$

• $g_n=g_{n-1}\cdot-4$

• $g_n=1\cdot-4^{n-1}$

• $a_n=1-4\left(n-1\right)$

Tags

CCSS.HSF.BF.A.2

Write an explicit formula for the arithmetic sequence:

5, 10, 15, 20, 25, ...

• $a_n=5+5\left(n-1\right)$

• $g_n=g_{n-1}\cdot2$

• $g_n=5\cdot2^{n-1}$

• $a_n=a_{n-1}+5$

Tags

CCSS.HSF.BF.A.2

Given the explicit formula, find  $a_5$  :

 $a_n=10-1\left(n-1\right)$  

• 14

• 5

• 6

• 15

Tags

CCSS.HSF.BF.A.2