Q. 84.0( 4 Votes )

Find the 20t

Answer :

Given: AP 3,8, 13,…,253


To find: The 20th term from the last term of the AP


Explanation:

The given AP is 3,8, 13,….,253


So, the first term is 3.


a = 3……(i)


Now finding the difference of the second and first term, we get


d = 8 – 3 = 5………(ii)


So the last term can be written as


an = 253


But we know an = a + (n – 1)d (standard form)


253 = a + (n – 1)d


Substituting the values from equation (i) and (ii), we get


253 = 3 + (n – 1)(5)


253 = 3 + 5n – 5


253 = 5n – 2


5n = 253 + 2


5n = 255


n = 51


Hence 253 is the 51st term of the given AP.


Now to the 20th term from last means 51 – 19 = 32nd term, as the last term is 51 – 0, second last term is 51 – 1, third last term is 51 – 2 and so on.


So 32nd term can be found from using the standard form formula, i.e.,

an = a + (n – 1)d, so


a32 = a + (32 – 1) d


Substituting values of a and d from equation (i) and (ii), we get


a32 = 3 + (31)(5)


a32 = 3 + 155


a32 = 158


Hence the 20th term from the last term of the AP is 158.


OR


Given: 7 times the 7th term of an A.P is equal to 11 times its 11th term


To find: its 18th term


Explanation: The standard form of an AP term is


an = a + (n – 1) d


Now the 7th term is,


a7 = a + (7 – 1) d

a= a + 6d……..(i)


And the 11th term is,


a11 = a + (11 – 1)d

a11 = a + 10d……..(ii)


And also the 18th term is,


a18 = a + (18 – 1)d

a18 = a + 17d……..(iii)


Now as per the given criteria,


7 times the 7th term of an A.P is equal to 11 times its 11th term.


7 × a7 = 11 × a11


Now substituting values from equation (i) and (ii), we get

 7 × (a + 6d) = 11 × (a + 10d)


7a + 42d = 11a + 110d


7a – 11a = 110d – 42d


– 4a = 68d



a = – 17d…….(iv)


Now substituting equation (iv) in equation (iii), we get


a18 = a + 17d


a18 = (–17d) + 17d

= 0


Hence the 18th term is 0.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses