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Arithmetic Progressions

Short Answer Type

291. A sum of Rs. 1000 is invested at 8% simple interest per year. Calculate the interest at the end of each year. Do these, interests form an A .P. ? If so, find the interest at the end of 30 yrs.

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292. In a flower bed, there are 23 rose plants in the first row, 21 in the second, 19 in the third and so on. There are 5 rose plant in the last row. How many rows are there in the flower bed?

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293. If m times the mth term of an A .P. is equal to n times its nth term show that (m + n)th term of the A .P. is zero.

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Long Answer Type

294. If the mth term of an A .P. is 1/n and the nth term is 1/m, find the (mn)th term.

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Short Answer Type

295. Split 69 into three parts such that they are in A .P. and the product of two smaller parts is 483.

Let the three parts, which are in A .P. be a – d, a, a + d
Case I.
a – d + a + a + d = 69
⇒ 3a = 69
a = 23 ...(i)
Case II. a (a – d) = 483 ...(ii)
Putting the value of (i) in (ii), we get
23 (23 - d) = 483
$rightwards double arrow space space space space space 23 minus straight d space equals 483 over 23 rightwards double arrow space space space space space 23 straight d minus straight d space equals space 21 rightwards double arrow space space space space space space space space space minus straight d space equals space minus 2 rightwards double arrow space space space space space space space space space space space space straight d space equals space 2$
Thus, the three parts are
a - d = 23 - 2 = 21
a = 23
and a + d = 23 + 2 = 25

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296. The ratio of the 7th to the 3rd term of an A .P. is 12 : 5. Find the ratio of the 13th to 4th term.

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297. If the Pth term of an A .P. is q and qth term is P, prove that its nth term is (P + q – n).

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298. Find the 10th term from the end of the A .P. 8, 10, 12................ 126

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299. The sum of the 4th and 8th terms of an A .P. is 24 and the sum of the sixth and tenth terms is 44. Find the First three terms of the A .P.

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300.

The first and the last term of an A .P. are 4 and 81 respectively. If the common difference is 7, how many terms are there in the A .P. and what is their sum?

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