1. Write down the stated term and the formula for the nth term of the following ...

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akaneyue1 @akaneyue1

September 2022 1 4 Report

1. Write down the stated term and the formula for the nth term of the following arithmetic sequences
a. 7, 11, 15, …(7th)
c. 18, 11, 4, … (6th )
b. -7, -5, -3, …(23rd)
d. 3, 3 ½, 4, … (16th)

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Verified answer

✏️SEQUENCES

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Direction: Write down the stated term and the formula for the nth term of the following arithmetic sequences:

a. 7, 11, 15, ... (7th)
b. 18, 11, 4, ... (6th)
c. -7, -5, -3, ... (23rd)
d. 3, 3½, 4 ... (16th)

Solution: Using this formula to find the common difference.

$\begin{aligned}&\bold{\color{lightblue}Formula:}\\ &\boxed{d = \frac{a_n - a_k}{n - k}} \end{aligned}$

- Using the Arithmetic Sequence Formula to find the nth term of the sequence:

$\begin{aligned}&\bold{\color{lightblue}Formula:}\\ &\boxed{a_n = a_1 + (n - 1)d} \end{aligned}$

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a. 7, 11, 15,... (7th)

- Determine the common difference.

$\begin{aligned}&{d = \frac{a_3 - a_1}{3 - 1}} \end{aligned}$

$\begin{aligned}&{d = \frac{15 - 7}{3 - 1}} \end{aligned}$

$\begin{aligned}&{d = \frac{8}{2}} \end{aligned}$

$d = 4$

- Find the 7th term.

$a_7 = 7 + (7 - 1)4$

$a_7 = 7 + (6)4$

$a_7 = 7 + 24$

$a_7 = 31$

$\therefore$ The 7th term of the arithmetic sequence is:

$\large \rm a_7 = \boxed{ \rm \green{ \: 31 \: }}$

$\rm$

b. 18, 11, 4, ... (6th)

- Determine the common difference.

$\begin{aligned}&{d = \frac{a_3 - a_1}{3 - 1}} \end{aligned}$

$\begin{aligned}&{d = \frac{4 - 18}{3 - 1}} \end{aligned}$

$\begin{aligned}&{d = \frac{ \text - 14}{2}} \end{aligned}$

$d = \text - 7$

- Find the 6th term.

$a_6 = 18 + (6 - 1) \: \text - 7$

$a_6 = 18 + (5) \: \text - 7$

$a_6 = 18 + (\text - 35)$

$a_6 = 18 - 35$

$a_6 = \text - 17$

$\therefore$ The 6th term of the arithmetic sequence is:

$\large \rm a_6 = \boxed{ \rm \green{ \: \text - 17 \: }}$

$\rm$

c. -7, -5, -3, ... (23rd)

- Determine the common difference.

$\begin{aligned}&{d = \frac{a_3 - a_1}{3 - 1}} \end{aligned}$

$\begin{aligned}&{d = \frac{ \text - 3 - ( \text - 7)}{3 - 1}} \end{aligned}$

$\begin{aligned}&{d = \frac{ \text - 3 + 7}{3 - 1}} \end{aligned}$

$\begin{aligned}&{d = \frac{4}{2}} \end{aligned}$

$d = 2$

- Find the 23rd term.

$a_{23} = \text - 7 + (23 - 1)2$

$a_{23} = \text - 7 + (22)2$

$a_{23} = \text - 7 + 44$

$a_{23} = 37$

$\therefore$ The 23rd term of the arithmetic sequence is:

$\large \rm a_{23} = \boxed{ \rm \green{ \: 37 \: }}$

$\rm$

d. 3, 3½, 4 ... (16th)

- Determine the common difference.

$\begin{aligned}&{d = \frac{a_3 - a_1}{3 - 1}} \end{aligned}$

$\begin{aligned}&{d = \frac{4 - 3}{3 - 1}} \end{aligned}$

$\begin{aligned}&{d = \frac{1}{2}} \end{aligned}$

- Find the 16th term.

$a_{16} =3 + (16 - 1) \frac{1}{2} \\$

$a_{16} =3 + (15) \frac{1}{2} \\$

$a_{16} =3 + \frac{15}{2} \\$

$a_{16} = \frac{6 + 15}{2} \\$

$a_{16} = \frac{21}{2} \\$

$a_{16} = 10 \ ½$

$\therefore$ The 16th term of the arithmetic sequence is:

$\large \rm a_{16} = \boxed{ \rm \green{ \: 10 \ ½ \: }}$

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