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The 4th term of an A.P. is zero. Prove that the 25th term of the A.P. is three times its 11th term - CBSE Class 10 - Mathematics

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Question

The 4th term of an A.P. is zero. Prove that the 25th term of the A.P. is three times its 11th term

Solution

4th term of an A.P.= a4 = 0

∴ a + (4 – 1)d = 0

∴ a + 3d = 0

∴ a = –3d ….(1)

25th term of an A.P. = a25

= a + (25 – 1)d

= –3d + 24d ….[From (1)]

= 21d.

3 times 11th term of an A.P. = 3a11

= 3[a + (11 – 1)d]

= 3[a + 10d]

= 3[–3d + 10d]

= 3 × 7d

= 21d

∴ a25 = 3a11

i.e., the 25th term of the A.P. is three times its 11th term.

  Is there an error in this question or solution?
Solution The 4th term of an A.P. is zero. Prove that the 25th term of the A.P. is three times its 11th term Concept: Arithmetic Progression.
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