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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.

We have, a₃ = 5
⇒ a + (3 – 1) d = 5
⇒ a + 2d = 5 ...(i)
and a₇ = 9
⇒ a + (7– n) d = 9
⇒ a + 6d = 9 ...(ii)
Subtracting (i) from (ii), we get
(a + 6d) – (a + 2d) = 4
⇒ a + 6d – a – 2d = 4
⇒ 4d = 4
⇒ d = 1
Putting the value of ‘d’ in (i), we get
a + 2d = 5 ⇒ a + 2(1) = 5
⇒ a + 2 = 5 ⇒ a = 3
Hence, the required A .P. be 3, 4, 5, 6, 7,...........

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

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280.

How many two digit numbers are divisible by 3.

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