Question

Find the 11th term of the last term ( towards the first term) of the arithmetic progression 10, 7, 4, .......-62

Answer 1

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

Here a = 10
d = 7 10 = -3

First lets find which term is 62

Let

a = -62
a + (n -1) d=-62

Putting values

10 + (n 1) (-3) =-62
10 + n (-3) 1(-3) = 62
10-3n+3 =-62
13- 3n=-62
-3n = -13 -62
-3n =-75
n=25

We need to find out 11th term from the last term

Last term = 25th

Second last term = 25 -1 = 24th
Third last term = 25 2 = 23rd

And so, on
So, 11th from last term = (25 10)th term

= 15th term
So, we need to find out a15

an = a + (n 1) d
Putting values

= 10 + (15 1) (-3)
15 = 10 + (14) 3)
= 10 42

= 32

So the 11th term from the Last = 15th term from the First = 32