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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.
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Case Study Push-ups are a fast and effective exercise for building strength. These are helpful in almost all sports including athletics. While the push-up primarily targets the muscles of the chest, arms, and shoulders, support required from other muscles helps in toning up the whole body.
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- Form an A.P representing the number of push-ups per day and hence find the minimum number of days he needs to practice before the day his goal is accomplished?
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