Question
If 100 times the 100th term of an AP with non zero common difference equals the 50 times its 50th term, then the 150th term of this AP is
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–150
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150
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times its 50th term
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0
Solution
D.
0
The 150 th term of this AP
Let a be the first term and d be the common difference of the given AP, then
T100 = a+ (100-1)d = a + 99d
T50 = a +(50-1)d = a +49 d
T150 = a + (150-1) d = a +149 d
Now, according to the question,
100 x T100 = 50 x T50
⇒ 100 (a +99d) = 50(a +49d)
2(a +99d) = (a+ 49d)
2a +198 d =a +49d
a +149d = 0