Find the 12th term from the end of the following arithmetic progressions:
(i) 3, 5, 7, 9, ... 201
(ii) 3, 8, 13, ..., 253
(iii) 1, 4, 7, 10, ..., 88
Answers
Answer:
The 12th term from the end of the A.P is 179.
The 12th term from the end of the A.P is 198.
The 12th term from the end of the A.P is 55.
Step-by-step explanation:
(i)
Given : 3,5,7,9,.....201
Let 'l' be the last term of an A.P
Common Difference , d = 5 -3 = 2,
Last term , l = 201
nth term from the end = l - (n - 1)d
12th term from the end = l - (n - 1)d
12th term from the end = 201 -(12 - 1)×2
12th term from the end = 201 - 11 × 2
12th term from the end = 201 - 22
12th term from the end = 179
Hence, the 12th term from the end of the A.P is 179.
(ii)
Given : 3,8 ,13,.....253
Let 'l' be the last term of an A.P
Common Difference , d = 8 - 3 = 5
Last term , l = 253
nth term from the end = l - (n - 1)d
12th term from the end = l - (n - 1)d
12th term from the end = 253 -(12 - 1)×5
12th term from the end = 253 - 11 × 5
12th term from the end = 253 - 55
12th term from the end = 198
Hence, the 12th term from the end of the A.P is 198.
(iii)
Given : 1,4 ,7,10,.....88
Let 'l' be the last term of an A.P
Common Difference , d = 4 - 1 = 3
Last term , l = 88
nth term from the end = l - (n - 1)d
12th term from the end = l - (n - 1)d
12th term from the end = 88 -(12 - 1)×3
12th term from the end = 88 - 11 × 3
12th term from the end = 88 - 33
12th term from the end = 55
Hence, the 12th term from the end of the A.P is 55
HOPE THIS ANSWER WILL HELP YOU...
as ap is from last
a =201
then d =a2-a1
d=7-9
=-2
so on putting the 12th term=
201+11x-2
201+{-22}
201-22
=179
ii)
iii) here.
a=1
d=4-1=3
now,
12th term = a+(n-1)d
=1+(12-1)3
=1+11×3
=34