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