SEQUENCE - the nth term of a sequence

ACADEMY"The reason many students fail mathematics is because they first fired the salvo of hatred and by the time the subject retaliated, they found it difficult to understand" E.A Adeboye
pH.D in applied Mathematics.





SEQUENCE 


A sequence is a succession of number stated in a definite order. Each of its member is formed and guided according to a definite rule. To solve a given sequence, you'll have to  think of a well define rule that satisfy the sequence.




Worked examples:

(1).       1, 3, 5, 7, 9.         (Rule: adding two to the preceding term)

1+2 =3, 
3+2 =5

(11).   2, 5, 8, 11,......(Rule: 3n - 1)

solo:   3(1) - 1 = 
             3 - 1 = 2,
3(2) - 1
= 6 - 1 = 5

 4,. 11, 30, 67,... ( Rule: n³+ 3)

1³ + 3 = 4,
2³ + 3 = 11

Hope you understand!




Solving For The ₙth Term Of A Sequence



The number occuring at the  place of a sequence is called the ₙth term of a sequence, we substitute for the number of  'n' in the given nth term formula. That is, a formula will be given and you'll substitute the number of  'n'  given in the formula.  A sequence do come with a define formula.



Worked examples


The ₙth term of a sequence is given as 3n² - 8n + 4. What is the 5th term?

solution:
The nth term Tₙ = 3n² - 8n+ 4 (the formula given)

Tₙ = 3(5)² - 8x5 + 4..  (substitute)
= 3x 25 - 8x5 + 4
75 - 40 +4 = 39




Example 11
if  the sum of the first nth term of a sequence given by n² ⁻ 2n + 4. Find the sum of the T₁ and T₅

solution 
Tₙ  = Sn - Sn - 1 ( the nth term of sequence as related to sum of a sequence)

Tₙ = n² - 2n +4 (the given formula )




Sₙ =  n² - 2n + 4

Sₙ ₋₁ = ( n - 1)² - 2(n -) + 4
= n² - 4n + 7 
hence, to gether will be

Tₙ = Sₙ - Sₙ ₋ ₁
Tₙ = n² - 2n +4 - ( n² -  4n + 7)
Tₙ = n² - 2n + 4 - n² +  4n - 7
= 2n - 3


Tₙ = 2n - 3
T₁ = 2( 1)
      2 - 1 = 1


T₅ = 2( 5) - 3
         10 - 3 = 7



Example 111

If for all integer nth  term a sequence is given as 

Uₙ ₊₁ = 1/3 ( Uₙ + 1) and U₁ = 1/3,find U₃

solution
Uₙ₊₁ = 1/3 (Uₙ + 1) ; U₁ = 1/3

U₂ = U₁ ₊₁ = 1/3 (U₁ +1) = 1/3 (1/3 +1) =1/3 x 4/3 = 4/9


U₃ = U₂ ₊₁ = 1/3 ( U₃ +1) = 1/3 (4/9 +1 ) = 1/3 x 13/9 = 13/27


Attempt this and send your answer in the comment section or through any of our social platform:


The nth term of a sequence is Tₙ = 5( n - 1)² . Evaluate T₄ ₋ T₆


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ESTHER GIFT is an ethusaitic and dynamic coach with great affinity for young minds and Students. She is a violence reader, who believes so much in her prowess to transmute a penetrating influence in the young ones and students. She has tremendously impacted lives across the globe through her articles with the use of scientific assertions and life tested principles that are bold enough to accelerate man beyond the sky of limitations. Her wealth of knowledge and passion is seen in DÆGESEAGE her company. SMS - STUDENTS' MONTHLY SERIES- a golden give away by DÆGESEAGE has massively reach and change lives amazingly. She was awarded recently by MINDCITY for excellence . In her vision to raise leaders she set up an annually quadrant LEADERSHIP AND EMPOWERMENT FORUM where she mentor upcoming leaders on how to lead with a privilege to master a handfull skill. Her vision lies in the young minds and students.Her aspirations is to lead them to a point of global relevance

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