Sequence
ေα‘ာα္αွာေαးαားαဲ့ αိα္းαα္းေαးαို ေα့αာαΎαα့္αေα‘ာα္။
1,4,9,16,25,...
α‘αုαိα္းαα္းαွာαါαα္αဲ့ αိα္းαံုးေαြαာ ေαးα်α္ααို ေαးαားျαα္း (random) ααုα္αါαူး။ αိα္းαံုးေαြ ေျαာα္းαဲαႈαွာ α αα ္αα ္αု (ααα္းေျαာααα္ function αα ္αု) α‘α ေျαာα္းαဲαြားαာαါ။ αါαို functional notation αဲαေျαာααα္αိုαα္...
f(1) = 1 = 12
f(2) = 4 = 22
f(3) = 9 = 32
f(4) = 16 = 42
f(5) = 25 = 52 αိုααိုႏိုα္αာေαါ။့
αါαိုαΎαα့္ျαα္းα‘ားျαα့္ function αဲ့ Domain αာ {1,2,3,4,5,...n}=the set of natural numbers αိုααါαα္။ αါαိုαα္ α‘αα္αါေျαာα္းαဲαႈαို αΎαα့္αံုαဲα function αဲ့ general formula αို α‘αြα္ααူ ေျαာႏိုα္αါαΏαီ။
f(n) = n2 ေαါ့...။
αါေαΎαာα့္ sequence αိုαာαာ special function αိုααိုႏိုα္αΏαီး αူαဲ့ domain αေαာ့ α‘αΏαဲαα္း ααာααိα္း α်ား αါαα္ေαာα‘α ု (the set of natural numbers) ျαα ္αါαα္။ image ေαြαိုေαာ့ αီေααာαွာ terms αိုα ေျαာα္းαဲေαααါαα္။ α‘ေααα‘ေαα ေျαာα္းαဲαႈαဲαα‘αူ α‘αံုးျαဳαα့္ symbols ေαြαိုαα္း ေျαာα္းαα္း αα္αွα္αါαα္။ α‘αα္αွာေαးαားαဲ့ αိα္းαံုးေαြαို α‘αုαိုေααေαα αα္αွα္αါαα္။
αီေααာαွာ nth term αို general term αိုαααုα္ general formula αိုααိုႏိုα္αါαα္။ αါေαΎαာα့္ sequence αို α‘αုαို definition αြα့္αိုႏိုα္αါαα္။
Sequence
A sequence is a function whose domain is either the set of all or part of natural numbers. The values (images) of function are called terms .
Example 1
Find the first four terms of the sequence defined by un = 3n - 5.
Solution
un = 3n - 5
u1 = 3(1) - 5 =-2
u2 = 3(2) - 5 = 1
u3 = 3(3) - 5 = 4
u4 = 3(4) - 5 = 7
Therefore the fist four terms are -2, 1, 4, 7.
Exercises
Find the first four terms of the sequence defined by
Example2
Which term of the sequence defined by un = 4n - 23 is 25?
Solution
un = 4n - 23
Let the nth term be 25.
Therefore un = 25
4n - 23 = 25
4n = 48
n = 12
Therefore the 12th term is 25.
ေα‘ာα္αွာေαးαားαဲ့ αိα္းαα္းေαးαို ေα့αာαΎαα့္αေα‘ာα္။
1,4,9,16,25,...
α‘αုαိα္းαα္းαွာαါαα္αဲ့ αိα္းαံုးေαြαာ ေαးα်α္ααို ေαးαားျαα္း (random) ααုα္αါαူး။ αိα္းαံုးေαြ ေျαာα္းαဲαႈαွာ α αα ္αα ္αု (ααα္းေျαာααα္ function αα ္αု) α‘α ေျαာα္းαဲαြားαာαါ။ αါαို functional notation αဲαေျαာααα္αိုαα္...
f(1) = 1 = 12
f(2) = 4 = 22
f(3) = 9 = 32
f(4) = 16 = 42
f(5) = 25 = 52 αိုααိုႏိုα္αာေαါ။့
αါαိုαΎαα့္ျαα္းα‘ားျαα့္ function αဲ့ Domain αာ {1,2,3,4,5,...n}=the set of natural numbers αိုααါαα္။ αါαိုαα္ α‘αα္αါေျαာα္းαဲαႈαို αΎαα့္αံုαဲα function αဲ့ general formula αို α‘αြα္ααူ ေျαာႏိုα္αါαΏαီ။
f(n) = n2 ေαါ့...။
αါေαΎαာα့္ sequence αိုαာαာ special function αိုααိုႏိုα္αΏαီး αူαဲ့ domain αေαာ့ α‘αΏαဲαα္း ααာααိα္း α်ား αါαα္ေαာα‘α ု (the set of natural numbers) ျαα ္αါαα္။ image ေαြαိုေαာ့ αီေααာαွာ terms αိုα ေျαာα္းαဲေαααါαα္။ α‘ေααα‘ေαα ေျαာα္းαဲαႈαဲαα‘αူ α‘αံုးျαဳαα့္ symbols ေαြαိုαα္း ေျαာα္းαα္း αα္αွα္αါαα္။ α‘αα္αွာေαးαားαဲ့ αိα္းαံုးေαြαို α‘αုαိုေααေαα αα္αွα္αါαα္။
| = | = | |||
| = | = | |||
| = | = | |||
| = | = | |||
| = | = | |||
| - - - - - - - - | - - | - - | - - | - - |
| = | = |
Sequence
A sequence is a function whose domain is either the set of all or part of natural numbers. The values (images) of function are called terms .
Example 1
Find the first four terms of the sequence defined by u
Solutionu
u
u
u
u
Therefore the fist four terms are -2, 1, 4, 7.
Exercises
Find the first four terms of the sequence defined by
| (a) un = 2n + 3 | (b) un = 3n2 - 2 | (c) un = 4n2+ 3n - 5 |
Which term of the sequence defined by u
Solutionu
Let the nth term be 25.
Therefore u
4n - 23
4n
n = 12
Therefore the 12th term is 25.
α
ာαα်αူ၏ α‘αြα်αို αေးα
ားα
ွာα
ောα့်αျှော်αျα်!
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