VERIFICAATION: Find the 9th term from the end of the AP 5, 9, 13,...., 185.

Question

Given: AP $\implies$5, 9, 13, ..., 185
Required: 9th term of AP from last
Solution: Let a be the first term, d the common difference, l the last term
We have d= a₂-a₁=9-5=4
d=4
Since a_n=a+(n-1)d
$\implies$ $ l= 5+(n-1)*4=185 $
$\implies$ $ 4n-4=180$
$\implies$ $n=46$
For 9^th term from last, n-9=46-9=37
$\implies$ 37 is the required term
$\therefore $$ a_{37}=5+(37-1)(4)=144+5=149$

---

But the correct answer turns out to be 153
where am i wrong?

Answer 1

Actually we need $(46-9+1)$th term

But we can use a more direct way:

The $9$th term from the end,

$$185+(9-1)\cdot(-4)=?$$