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Arithmetic Progressions

Short Answer Type

271. The nth term of an A .P. is 7 – 4n find its common difference.

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

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

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

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

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

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

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279. Find the middle term of the A .P. 10,7,4, ...... (– 62).

We have, a_n = –62,
a = 10 and d = –3 Now a_n = a + (n – 1)d
⇒ –62 = 10 + (n – 1) (– 3)
⇒ – 62 = 10 – 3n +3
⇒ – 62 = 13 – 3n
⇒ –3n = –75
⇒ n = 25
Now middle term = a₁₃ = a + 12d
= 10 + 12(– 3)
= 10 – 36 = – 26

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280.

How many two digit numbers are divisible by 3.

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