First slide

Arithmetic progression

Question

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

Moderate

A

0
B

22
C

220
D

198

Solution

$\begin{array}{l} 9 t_{9} = 13 t_{13} \\ 9 (a + 8 d) = 13 (a + 12 d) \\ 9 a + 72 d = 13 a + 13 (12) d \\ (- 4 a) = (156 - 72) d = 84 d \\ a = - 21 d \\ t_{22} = a + 21 d = 0 \end{array}$

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