Question 1:Find the sum of odd integers from 1 to 2001.
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Question 2:Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.
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Question 3:In an A.P., the first term is 2 and the sum of the first five terms is one-fourth of the next five terms. Show that 20th term is –112.
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Question 4:How many terms of the A.P. – 6, 11 2 − , – 5, … are needed to give the sum –25?
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Question 5:In an A.P., if pth term is 1 q and qth term is 1 p , prove that the sum of first pq terms is 1 2 (pq +1), where π ¹ q.
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Question 6:If the sum of a certain number of terms of the A.P. 25, 22, 19, … is 116. Find the last term.
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Question 7:Find the sum to n terms of the A.P., whose kth term is 5k + 1.
Question 8:If the sum of n terms of an A.P. is (pn + qn2), where π and q are constants, find the common difference.
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Question 9:The sums of n terms of two arithmetic progressions are in the ratio 5n + 4 : 9n + 6. Find the ratio of their 18th terms.
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Question 10:If the sum of first π terms of an A.P. is equal to the sum of the first q terms, then find the sum of the first (p + q) terms.
EXERCISE 9.21. Find the sum of odd integers from 1
Question 11:Sum of the first p, q and r terms of an A.P. are a, b and c, respectively. Prove that ( ) ( ) ( ) 0 a b c q r r π p q p q r − + − + − =
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Question 12:The ratio of the sums of m and n terms of an A.P. is m2 : n2. Show that the ratio of mth and nth term is (2m – 1) : (2n – 1).
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Question 13:If the sum of n terms of an A.P. is 3n2 + 5n and its mth term is 164, find the value of m.
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Question 14:Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
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Question 15:If 1 1 n n n n a b a b − − + + is the A.M. between a and b, then find the value of n.
