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Arithmetic and Harmonic Sequence Calculation: Finding Terms and Differences, Cheat Sheet of Mathematics

Mathematics

CalculusÁlgebraNumber Theory

Examples of calculating terms in arithmetic and harmonic sequences using given first terms, differences, and desired terms. It includes step-by-step calculations for various sequences and terms.

What you will learn

How do you find the 15th term in a harmonic sequence given the first term and common difference?
What is the formula for finding the nth term in a harmonic sequence?
How do you find the 15th term in an arithmetic sequence given the first term and common difference?

What is the formula for finding the nth term in an arithmetic sequence?
How do you find the common difference in an arithmetic sequence given the first term and the third term?

Typology: Cheat Sheet

2019/2020

Uploaded on 05/15/2022

nina-soco 🇵🇭

1 / 13

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Partial preview of the text

Download Arithmetic and Harmonic Sequence Calculation: Finding Terms and Differences and more Cheat Sheet Mathematics in PDF only on Docsity! NINA FAITH SOCO 10-SAPPHIRE # EXAMPLE OF # _ ARITHMETIC yy SEQUENCE 4. 0/ 2.)a7=28 a13=20 (find the 15th term)an=a1+(n-1)d a7=a1+(7-1)d 28=a1+6d Equation # 1 an=a1+(n-1)d a13=a1+(13-1)d 20=a1+12d Equation #2 28=a1+6d 20=a1+12d ----------------- -8 -4d ---- ------ -4 -4d 2-D ; D=2 2.)a7=28 a13=20 (find the 15th term) a7=a1+(n-1)d a7=a1=(7-1)2 28=a1+(6)2 28=a1+12 28-12=a1 16=a1 ; a1=16 a15=a1+(n-1)d a15=16+(15-1)2 a15=16+(14)2 =16+28 a15=44 a15=44 3.) a1=-10 d=15 (find the 3th term)a3=a1+(n-1)d a3=-10+(3-1)15 a3=-10+(2)15 a3=-10+30 a3=20 a3=20 1)a2=1/6 ; a4=1/12 (find the 13th term)an=a1+(n-1 d a2=a1+(2-1)3 5=a1+(1)3 5=a1+3 5-3=a1 2=a1 ; a1=2 a13=a1(n-1)d a13=2+(12-1)3 =2+(11)3 =2+33 a13=35 ) 2.)a3=1/5 a5=1/25 (find the 9th term)an=a1+(n-1)d a3=a1+(3-1)d 5=a1+2d Equation #1 an=a1+(n-1)d a5=a1+(5-1)d 25=a1+4d Equation #2 5=a1+2d 25=a1+4d --------------- -20 -2d ----- ------ -2 -2d 10=D ; D=10 2.)a3=1/5 a5=1/25 (find the 9th term)a3=a1+(n- 1)d a3=a1+(3- 1)10 5=a1+(2)10 =a1+20 5-20=a1-15=a1 ; a1=-15 a9=a1+(n-1)d a9=-15+(9-1)10 =-15+(8)10 =-15+80 a9=65

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