Question 3 Find the eleventh term from the last term of the AP: 27, 23, 19, ..., 65.AP is 27, 23, 19, , 65
Here a = 27
d = 23 27 = 4
First lets find which term is 65
Let
an = 65
a + (n 1) d = 65
Putting values
27 + (n 1) ( 4) = 65
27 + n ( 4) 1( 4) = 65
27 4n + 4 = 65
27 4n + 4 = 65
31 4n = 65
4n = 65 31
4n = 96
n = ( 96)/( 4)
n = 24
We need to find out 11th term from the last term
Last term = 24th
Second last term = 24 1 =23th
Third last term = 24 2 = 22nd
And so, on
So, 11th from last term = (24 10)th term .
= 14th term
So, we need to find out a14
an = a + (n 1) d
Putting values
a14 = 27 + (14 1) ( 4)
a14 = 27 + (13) ( 4)
= 27 52
= 25
So, 11th term from the last = 14th term from the first
= 25
Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.
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