Find the twentieth and the nth of the sequence 4,9,14,19,....

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

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4,9,14,19,....a20,...an

We notice that the differenc ebetween terms is 5

==> r= 5

a1= 4

a2= 4+ 5 = 9

a3= 4+ 2(5) = 14

......

a20 = 4 + 19(5) = 99

an = a1 + (n-1)*r

      = 4 + (n-1)*5

      = 4+ 5n - 5

      = 5n -1

==> an = 5n -1

crmhaske's profile pic

crmhaske | College Teacher | (Level 3) Associate Educator

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First we have to find the difference between terms:

an = a1 + (n-1)d
d = (an - a1) / (n -1)
= (9 - 4) / 1
= 5

To test that this is an arithmetic series we can determine whether the differences are the same for the other two terms:

d = (14 - 4) / 2 = 5
d = (19 - 4) / 3 = 5

So it is an arithmetic series.  From here solving for a20 is as simple as using the same expression:

a20 = a1 + (20 - 1)d
a20 = 4 + 19(5)
a20 = 99

Top Answer

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

Before any calculus of  any term, we'll have to establish if the sequence is an arithmetical progression or geometric progression.

We notice that the difference between 2 consecutive terms is:

9-4 = 5

14-9 = 5

19-14 = 5

.................

So, the sequence is an arithmetical progression where the first term a1 = 4 and the common difference, d = 5.

We'll apply the formula of finding the n-th term of the a.p.

an = a1 + (n-1)*d

an = 4 + (n-1)*5

Substituting n by the value 20, we could calculate the 20th term of the a.p.

a20 = a1 + (20-1)*5

a20 = 4 + 19*5

a20 = 4 + 95

a20 = 99

munshifa's profile pic

munshifa | Student, Grade 10 | eNotes Newbie

Posted on

same as like this questions,please answer for this .'Find n if nth term of the AP 4,9,14,19...is 24.

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

The given sequence  4,9,14,19.

T2 -T1 = 9-4 =5.

T3-T2 = 14-9 =5

T4-T3 = 19-14 =5

This is an AP.So the successive terms have the common difference  d = 5.

The  nth term Tn = T1 + (n-1) d.

n =20

20 th term = T20 = T1 +(20-1)d = 4 +(20-1)*5 = 4+19*5 = 99

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