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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 ______.
Options
0
22
220
198
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Solution
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.
Explanation:
Tn = a + (n – 1)d
∴ T9 = a + 8d
And T13 = a + 12d
As per the given condition
9[a + 8d] = 13[a + 12d]
⇒ 9a + 72d = 13a + 156d
⇒ – 4a = 84d
⇒ a = – 21d .....(i)
Now T22 = a + 21d
= – 21d + 21d
= 0 ....[From equation (i)]
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