If 100 times the 100th term of an AP with non-zero common difference equals 50 times its 50th term, then the 150th term of this AP is: - Mathematics MCQ AIEEE 2012 2026 | ExamTest.live | ExamTest.live

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If 100 times the 100th term of an AP with non-zero common difference equals 50 times its 50th term, then the 150th term of this AP is:

A $-150$
B $150 times its 50th term$
C $150$
D $zero$

Solution & Step-by-step Explanation

Let the first term be a and the common difference be d . T_{100} = a + 99 d T_{50} = a + 49 d Given: 100 (a + 99 d) = 50 (a + 49 d) Divide by 50: 2 (a + 99 d) = a + 49 d 2 a + 198 d = a + 49 d a + 149 d = 0 The 150th term T_{150} = a + (150 - 1) d = a + 149 d .Since a + 149 d = 0, T_{150} = 0 .

Practice this question

Try it yourself before checking the explanation above.

If 100 times the 100th term of an AP with non-zero common difference equals 50 times its 50th term, then the 150th term of this AP is:

A

-150

B

150 times its 50th term

C

150

D

zero

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Arithmetic Progression Sequences and Series

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