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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?

Two digits numbers, which are divisible by
7 are, 14, 21, 28.......... 98.
Here, a = 14, d = 7 and l = 98
We know that, Tn = a + (n –1)d
⇒ 98 = 14 + (n – 1) (7)
[∵ l = T_n]
⇒ 98 = 14 + 7n – 7
⇒ 98 = 7n + 7
⇒ 98 = 7 = 7n
⇒ 91 = 7n ⇒ n = 13
Hence, number of terms (n) = 13.

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