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 is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.