Question

for the finite AP 3,5,7,...,201 , find the 12th term feom the end.

Answer 1

Let the first term be a

difference be d.

Lets make the AP

201,199,197.......3

a=201

let the d be -2

12th term is a+11d

=201+11(-2)

=201-22

=179

This is 12 th term from the back of that AP 3,5,......201

Hope it helps

Answer 2

Here, $a_{1} = 3 \\ a_{2} = 5 \\ \\ d = a_{2} - a_{1} \\ d = 5 - 3 \\ d = 2 \\ a_{n} = 201$

Since we are asked to find the 12th term from the end.

So, the Arithmetic Progression series for this will be :

$a = 201 \\ d = - 2 \: \: (since \: the \: series \: \\ \: must \: be \: from \: the \: end) \\ \\ a_{2} = a + d \\ a_{2} = 201 + (- 2) \\ a_{2} = 199 \\ \\ a_{3} = a + 2d \\ a_{3} = 201 + 2( - 2) \\ a_{3} = 201 - 4 \\ a_{3} = 197 \\ n = 12 (Given)$

201, 199, 197, 195, ..., 3

Putting the values in the formula :

$\bf a_{n} = a + (n - 1)d \\ \\ a_{12} = 201 + (12 - 1) \times - 2 \\ \\ a_{12} = 201 + (11) \times - 2 \\ \\ a_{12} = 201 - 22 \\ \\ a_{12} = 179$

If any doubt, please ask ;)