Question

find the 11th term frm the last term of th3 AP 10,7,4,.......-62.

Answer 1

n = 11

a = -62 ( as we have to find 11th term from end )

d = 3

a11 = a + 10d

= -62 + 10*3

= -62 + 30

= - 32

or 

nth term from end of an ap = l - ( n - 1 ) d

l is the last term of ap

= -62 -  ( 11 - 1 ) -3

= -62 - 10* -3

-62 + 30

=-32

Answer 2

Given ,

AP : 10, 7, 4,........-62

Here,

First term , a = 10

Common Difference , d = (7 - 10) = -3

Last term , L = -62

Therefore,

L = 10 + ( n-1 ) × (-3)

=> -62 = 10 + n ( -3 ) - 1 × (-3)

=> -62 = 10 - 3n + 3

=> -65 = 10 - 3n

=> -65 - 10 = -3n

=> -75 = -3n

Thus n = 25

Now, 11 th term from the last term

= ( 25 - 11 + 1 ) th term from the beginning

= 15th term from the beginning

So,

a 15 = 10 + ( 15 - 1 )(-3)

= 10 + 14 (-3)

= 10 - 42

= -32

i.e. The 11 th term from the last term is -32

^_^