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2. Sequences and series of real numbers
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Q1 of 110 Page 53

Find the sum of the first (i) 75 positive integers (ii) 125 natural numbers.

(i) In the A.P.


First term = 1


No. of terms = 75


Common difference = 1


Sum of terms =


⇒ Sum of terms =


⇒ Sum of terms =


⇒ Sum of terms = 2850


(ii) In the A.P.


First term = 1


No. of terms = 125


Common difference = 1


Sum of terms =


⇒ Sum of terms =


⇒ Sum of terms =


⇒ Sum of terms = 7875


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14

If a, b, c, d are in a geometric sequence, then show that (a - b + c) (b + c + d) = ab + bc + cd.

15

If a, b, c, d are in a G.P., then prove that a + b, b + c, c + d, are also in G.P.

2

Find the sum of the first 30 terms of an A.P. whose nth term is 3 + 2n.

3

Find the sum of each arithmetic series

(i) 38 + 35 + 32 + … + 2. (ii) terms.

Questions · 110
2. Sequences and series of real numbers
1 2 3 4 5 6 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 1 1 1 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 2 3 4 5 6 7 8 9 10 11 12 1 1 1 1 1 1 2 2 3 4 5 6 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
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