7, ... (20th term) WITH SOLUTION PLEASE THANKS...

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October 2022 1 14 Report

harmonic sequence find the nth term indicated inside the parenthesis.

4/5, 1/2, 4/11, 2/7, ... (20th term)

WITH SOLUTION PLEASE THANKS

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UK2019

Verified answer

✏️SEQUENCES

$\red{••••••••••••••••••••••••••••••••••••••••••••••••••}$

$\underline{\mathbb{DIRECTION:}}$

- Find the nth term indicated inside the parentheses.

4/5, 1/2, 4/11, 2/7, ... (20th term)

$\red{••••••••••••••••••••••••••••••••••••••••••••••••••}$

$\underline{\mathbb{ANSWER:}}$

$\qquad\begin{gathered}\LARGE\rm» \:\: \green{a_{20} = \frac{2}{31}}\end{gathered}$

$\red{••••••••••••••••••••••••••••••••••••••••••••••••••}$

$\underline{\mathbb{SOLUTION:}}$

- Find the reciprocal of the first four terms so that we will get the arithmetic terms.

$\frac{5}{4}, \: 2, \: \frac{11}{4}, \: \frac{7}{2} \\$

- Determine the common difference by using the formula.

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

$\begin{aligned}{d=a_2-a_{1} = 2 - \frac{5}{4} = \frac{8 - 5}{4} = \frac{3}{4} }\end{aligned}$

$\begin{aligned}{d=a_3-a_{2} = \frac{11}{4} - 2 = \frac{11 - 8}{4} = \frac{3}{4} }\end{aligned}$

$\begin{aligned}{d=a_4-a_{3} = \frac{7}{2} - \frac{11}{4} = \frac{14-11}{4} = \frac{3}{4} }\end{aligned}$

- The common difference is 3/4. Using the Harmonic Sequence Formula to find 20th term of the sequence.

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

$\begin{aligned}{a_{20} = \frac{1}{ \frac{5}{4} + (20 - 1) \frac{3}{4} }}\end{aligned}$

$\begin{aligned}{a_{20} = \frac{1}{ \frac{5}{4} + (19) \frac{3}{4} }}\end{aligned}$

$\begin{aligned}{a_{20} = \frac{1}{ \frac{5}{4}+\frac{57}{4} }}\end{aligned}$

$\begin{aligned}{a_{20} = \frac{1}{\frac{62}{4} }}\end{aligned}$

$\begin{aligned}{a_{20} = \frac{1}{\frac{31}{2} }}\end{aligned}$

- Find the reciprocal of 31/2 since the denominator have fraction.

$\begin{aligned}{a_{20} = \frac{2}{31}}\end{aligned}$

$\therefore$ The 20th term of the harmonic sequence is 2/31.

$\red{••••••••••••••••••••••••••••••••••••••••••••••••••}$

#CarryOnLearning

jaymargallo hi po ate o kuya :) kamusta po?

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✏️SEQUENCES

Add an Answer

hi po moderators pa help naman po sa math please thank u47a166e6abe83e98cb0b6dcf856a79e3 24430

Pagsusuri: Anong anyo ng pagsusuring pampanitikan ang nobela? Patunayan ang iyon...

please dont answer if youre answer is nonsense not helpful copying because745cb39828ac16abd6a6cdaf8ad28eb4 85864

how to find the ratio of the geometric sequence

hi! ace, genius and moderators! kindly help me in my Science? please don't waste...

hi! ace, genius and moderators! kindly help me in my Science? please don't waste...

hi! ace, genius and moderators! kindly help me in my Science? please don't waste...

hi! ace, genius and moderators! kindly help me in my Science? please don't waste...

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