Find the 20th term from the last term of the AP : 3, 8, 13, . . ., 253.

Question

Homi · Accepted Answer

We need to find a specific term from the end of the given sequence.

Step 1 — Find AP details

Let's first identify the key values of our Arithmetic Progression. The first term is $a$ . The common difference is $d$ . The last term is $l$ .

$a = 3$

$d = 8 - 3$

$\boxed{d = 5}$

The last term given is 253.

Step 2 — Reverse the AP

To find a term from the last, we can reverse the AP. The last term becomes the new first term. The common difference changes its sign.

Let the new first term be $a'$ . Let the new common difference be $d'$ .

$a' = 253$

$d' = -5$

We need to find the 20th term of this new AP.

Step 3 — Calculate the 20th term

The $n$ -th term formula is $a_n = a + (n-1)d$ . We use $a'$ as the first term. We use $d'$ as the common difference. We want to find the 20th term, so $n = 20$ .

$a_{20} = a' + (20-1)d'$

$a_{20} = 253 + (19)(-5)$

$a_{20} = 253 - 95$

$\boxed{a_{20} = 158}$

Answer

The 20th term from the last is 158.

Question 17

Answer

More questions in Exercise 5.2