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.
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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.
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?
Let ‘a’ be the first term, ‘d’ be the common difference and ‘l’ be the last term. Then.
Hence, there are 12 terms in the A .P. and their sum is 510.
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