If 9 times the 9th term of an A.P. is equal to 13 times the 13th term, then the 22nd term of the A.P. is

Question

If 9 times the 9th term of an A.P. is equal to 13 times the 13th term, then the 22nd term of the A.P. is (A) 0 (B) 22 (C) 220 (D) 198

Tardigrade Admin · Accepted Answer

Let 1st term of A.P. = a and common difference = d Given, 9 × a9 = 13 × a13 ⇒ 9(a + 8d) = 13(a + 12d) ⇒ 4a + 84d = 0 ⇒ a + 21 d = 0 Now, a22 = a + 21d = 0

Q. If $9$ times the $9^{t h}$ term of an $A . P$ . is equal to $13$ times the $1 3^{t h}$ term, then the $2 2^{n d}$ term of the $A . P$ . is

$0$

$22$

$220$

$198$

Let $1^{s t}$ term of $A . P . = a$ and common difference $= d$
Given, $9 \times a_{9} = 13 \times a_{13}$
$\Rightarrow 9 (a + 8 d) = 13 (a + 12 d)$
$\Rightarrow 4 a + 84 d = 0$
$\Rightarrow a + 21 d = 0$
Now, $a_{22} = a + 21 d = 0$

Q. If 9 times the 9th term of an A.P. is equal to 13 times the 13th term, then the 22nd term of the A.P. is

0

22

220

198

Let 1st term of A.P.=a and common difference =d Given, 9×a9​=13×a13​ ⇒9(a+8d)=13(a+12d) ⇒4a+84d=0 ⇒a+21d=0 Now, a22​=a+21d=0

Q. If $9$ times the $9^{t h}$ term of an $A . P$ . is equal to $13$ times the $1 3^{t h}$ term, then the $2 2^{n d}$ term of the $A . P$ . is

$0$

$22$

$220$

$198$

Let $1^{s t}$ term of $A . P . = a$ and common difference $= d$
Given, $9 \times a_{9} = 13 \times a_{13}$
$\Rightarrow 9 (a + 8 d) = 13 (a + 12 d)$
$\Rightarrow 4 a + 84 d = 0$
$\Rightarrow a + 21 d = 0$
Now, $a_{22} = a + 21 d = 0$