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Let a be the first term and d be the common difference of the A .P. we have, a 9 = 0 ⇒ a + 8d = 0 ⇒ a = – 8d Now, a 29 = a + 28d = –8d + 28d = 20d 2(a 19 ) = 2(a + 18d) = 2(– 8d + 18d) = 2(10d) = 20d Hence, a 29 = 2 (a 19 )

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Arithmetic Progressions

Short Answer Type

281. Write the common difference of an A .P. whose nth term is 3n + 5.

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282. For what value of k, are the numbers x, 2x + k and 3x + 6 three consecutive terms of an A .P

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283. The 17th term of an A .P. exceeds its 10th term by 7. Find the common difference.

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284. If 9th term of an A .P. is zero. Prove that 29th term is double of its 19th term.

Let a be the first term and d be the common difference of the A .P. we have,
a₉ = 0 ⇒ a + 8d = 0 ⇒ a = – 8d
Now, a₂₉ = a + 28d = –8d + 28d = 20d
2(a₁₉) = 2(a + 18d) = 2(– 8d + 18d)
= 2(10d) = 20d
Hence, a₂₉ = 2 (a₁₉)

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285. If 5th term of an A .P. is zero. Prove that its 23rd term is three times its 11th term.

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286. How many numbers of two digits are divisible by 7?

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287. Which term of the A .P. 3, 15, 27, 39 ... will be 120 more than its 21st term?

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288. Which term of the A .P. 4, 12, 20, 28, ... will be 120 more than its 21^st term?

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289. Determine the A .P. whose 3rd term is 5 and the 7th term is 9.

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290. How many two digit numbers which are multiples of 5 lie between 10 and 100 ?

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