NINA FAITH
SOCO
10-SAPPHIRE
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Arithmetic and Harmonic Sequence Calculation: Finding Terms and Differences, Cheat Sheet of Mathematics
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.
Typology: Cheat Sheet
2019/2020
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NINA FAITH
SOCO
10-SAPPHIRE
3 EXAMPLE OF ARITHMETIC SEQUENCE
1) 1) a3=10 a5=40 (find the 15th term)
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
28=a1+6d 20=a1+12d
-8 -4d
-4 -4d 2-D ; D=
3.) a1=-10 d=15 (find the 3th term) a3=a1+(n-1)d a3=-10+(3-1) a3=-10+(2) a3=-10+ a3=
a3=
3 EXAMPLE OF harmonic SEQUENCE
1)a2=1/6 ; a4=1/12 (find the 13th term)an=a1+(n-1)d a2=a1+(2-1) 5=a1+(1) 5=a1+ 5-3=a 2=a1 ; a1= a13=a1(n-1)d a13=2+(12-1) =2+(11) =2+ a13=
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 # an=a1+(n-1)d a5=a1+(5-1)d 25=a1+4d Equation # 5=a1+2d 25=a1+4d
-20 -2d
-2 -2d 10=D ; D=
3.)a1=1/10 ; D=2 (find the 20th term) a20=a1+(n-1)d =10+(20-1) =10+(19) =10+ a20=