Arithmetic Sequences and Series

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ARITHMETIC SEQUENCES AND SERIES




3 ; 8 ; 13 ; … (ARITHMETIC SEQUENCE)


3 ; 9 ; 27 ; … (GEOMETRIC SEQUENCE)


SEQUENCE: A SET OF REAL NUMBERS IN A _______________________ IS
CALLED A SEQUENCE.




𝑇1 ; 𝑇2 ; 𝑇3 ; 𝑇4 ; … ; 𝑇𝑛
; ; ; ; … ;
; ; ; ; … ;
; ; ; ; … ;
; ; ; ; … ;


ARITHMETIC SEQUENCE:
If and are real numbers, then
; ; ; ;
is an arithmetic sequence with:
𝑎=
𝑑=
𝑇𝑛 =

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1. Find the 4th term of the arithmetic sequence:
7 ; 3 ; …
Solution:




1 1
2. Find 𝑇10 of 4 ; 1 ; −1 ; −3
2 2
Solution:

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3. Find the 7th term of the sequence 2 ; 5 ; 8 ; …
Solution:




Do a check:
𝑇1 𝑇2 𝑇3 𝑇4 𝑇5 𝑇6 𝑇7

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3 1
4. Find the 8th term of the sequence −4 ; −1 ; ; …
4 2
Solution:




REVERSE PROCESS !
5. Which term of the sequence 4 ; 9 ; 14 ; … will be 34?
Solution:

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6. How many terms are there in the sequence 3 ; 7 ; 11 ; … ; 147
Solution:




7. Which term of the arithmetic sequence 10 ; 7 ; … is −5?
Solution:

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8. How many terms are there in the sequence:

3 1 3
45 ; 43 ; 42 ; … ; 33
4 2 4
Solution:

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SIMULTANEOUS EQUATIONS
9. The 12th term of an arith. sequence is −5 and the 20th term is 7.
Find the 7th term.
Solution:

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10. The 7th term of an arith. sequence is 20 and the 13 th term is 38.
Find the first 3 terms.
Solution:

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11. In an arith. sequence the 7 th term is 30 and the 4th term is 18.
Find the 1st term and the common difference.
Solution:

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12. Find the 20th term of an arith. sequence if the 5 th term is 11 and the
12th term is 25.
Solution: