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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?

Here a = 4, d = 12 – 4 = 8. Then = a + 20d = 4 + 20 x 8 = 4 + 160 = 164
Let a_n be 120 more than its 21^st term

$therefore space space space space space space space straight a subscript straight n space equals space 164 plus 120 equals 284 rightwards double arrow space space space space space space space straight a left parenthesis straight n minus 1 right parenthesis straight d equals 284 rightwards double arrow space space space space space space 4 plus left parenthesis straight n minus 1 right parenthesis cross times 8 equals 284 rightwards double arrow space space space space space space 8 left parenthesis straight n minus 1 right parenthesis space equals space 280 rightwards double arrow space space space space space space space straight n minus 1 equals 280 over 8 equals 35 rightwards double arrow space space space space space space space space space space straight n space equals space 35 space plus space 1 space equals space 36$
Hence, 36^th term is 120 more than its 21^st term.