Express the following numbers as the sum of odd numbers using the abov

1.	Express the following numbers as the sum of odd numbers using the above pattern?(a) 63 (b) 83 (c) 73Consider the following pattern.23-13 =1+ 2 x 1 x 333-23 =1+ 3 x 2 x 343-33 =1+ 4 x 3 x 3Using the above pattern, find the value of the following.(i) 73-63 (ii) 123-113 (iii)203-193 (iv) 513-503
Answer» (a) n=6 and (n-1) = 5 ∴ We start with (6 x 5) + 1 = 31 we have 6³= 31 + 33 + 35 + 37 + 39 + 41=216 (b) n=8 and (n-1)=7 ∴ we start with (8 x 7)+1=57 we have 8³= 57 + 59 + 61 + 63 + 65 + 67 + 69 + 71 = 512 (c) n = 7 and (n-1) =6 ∴ we start with (7 x 6) + 1 = 43 We have 7³= 43+ 45+ 47 + 49 + 51 + 53 + 55 = 343 (i) 7³-6³= 1 + 7 x 6 x 3 = 127 (ii) 12³-11³= 1 + 12 x 11 x 3 = 397 (iii) 20³-19³= 1 + 20 x 19 x 3 = 1141 (iv) 51³-50³= 1 + 51 x 50 x 3 = 7651

Express the following numbers as the sum of odd numbers using the above pattern?(a) 63 (b) 83 (c) 73Consider the following pattern.23-13 =1+ 2 x 1 x 333-23 =1+ 3 x 2 x 343-33 =1+ 4 x 3 x 3Using the above pattern, find the value of the following.(i) 73-63 (ii) 123-113 (iii)203-193 (iv) 513-503

Answer»

(a) n=6 and (n-1) = 5
∴ We start with (6 x 5) + 1 = 31
we have
6³= 31 + 33 + 35 + 37 + 39 + 41=216
(b) n=8 and (n-1)=7
∴ we start with (8 x 7)+1=57
we have
8³= 57 + 59 + 61 + 63 + 65 + 67 + 69 + 71 = 512
(c) n = 7 and (n-1) =6
∴ we start with (7 x 6) + 1 = 43
We have
7³= 43+ 45+ 47 + 49 + 51 + 53 + 55 = 343

(i) 7³-6³= 1 + 7 x 6 x 3 = 127
(ii) 12³-11³= 1 + 12 x 11 x 3 = 397
(iii) 20³-19³= 1 + 20 x 19 x 3 = 1141
(iv) 51³-50³= 1 + 51 x 50 x 3 = 7651

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Express the following numbers as the sum of odd numbers using the above pattern?(a) 63 (b) 83 (c) 73Consider the following pattern.23-13 =1+ 2 x 1 x 333-23 =1+ 3 x 2 x 343-33 =1+ 4 x 3 x 3Using the above pattern, find the value of the following.(i) 73-63 (ii) 123-113 (iii)203-193 (iv) 513-503

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