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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.

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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 ?

The list of two digit numbers which are multiples of 5 are
15, 20, 25, 30,...........95
We have, a = 15, d = 5, a_n = 95
We know, a_n = a + (n – 1) d
⇒ 95 = 15 + (n – 1)5
⇒ 95 = 15 + 5n – 5
⇒ 95 = 10 + 5n
⇒ 5n = 85
⇒ n = 17
Hence, there are 17 two digit numbers lie between 10 and 100 which are multiples of 5.

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