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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.

Here, P = 1000, r = 8%
Interest at the end of first year.

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Interest at the end of second year

$equals fraction numerator straight P cross times straight r cross times straight t over denominator 100 end fraction equals space fraction numerator 1000 cross times 8 cross times 2 over denominator 100 end fraction equals R s. space 160$
Interest at the end of third year

$equals fraction numerator straight P cross times straight r cross times straight t over denominator 100 end fraction equals fraction numerator 1000 cross times 8 cross times 3 over denominator 100 end fraction equals space Rs. space 240$
So, we have 80, 160, 240, ..............
Here, a = 80, d = 80
Therefore, interest at the end of 30 yrs. i.e. a₃₀ is,
a₃₀ = a + (30 –1) d = 80 + 29 x 80
= 80 + 2320 = 2400
So the interest at the end of 30 years is Rs. 2400.

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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.

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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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