Find the twentieth and the nth of the sequence 4,9,14,19,....
5 Answers
hala718 | High School Teacher | (Level 1) Educator Emeritus
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 | College Teacher | (Level 3) Associate Educator
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
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 | Student, Grade 10 | eNotes Newbie
same as like this questions,please answer for this .'Find n if nth term of the AP 4,9,14,19...is 24.
neela | High School Teacher | (Level 3) Valedictorian
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