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Find the sum of the first 25 terms of each of the arithmetic sequences below. i. 11, 22, 33,…. ii. 12, 23, 34,… iii. 21, 32, 43,…. iv. 19, 28, 37,… vi. 1, 6, 11,…. |
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Answer» i. 11, 22, 33, ...... Common difference a = 22 - 1 1 = 11 First term = 11 a + b = 11 b = 11 - 11 = 0 n = 25 Sum = 1/2 an (n + 1) + nb = 1/2 x 11 x 25 x 26 + 25 x 0 = 3575 ii. 12, 23, 34, ...... Common difference a = 23 - 1 2 = 11 First term = 12 a + b = 12 b = 12 - 11 = 1 n = 25 Sum = 1/2 an (n + 1) + nb = 1/2 x 11 x 25 x 26 + 25 x 1 = 3600 iii. 21, 32, 43, ...... Common difference a = 32 - 2 1 = 11 First term = 21 a + b = 21 b = 21 - 11 = 10 n = 25 Sum = 1/2 an (n + 1) + nb = 1/2 x 11 x 25 x 26 + 25 x 10 = 3825 iv. 19, 28, 37, ...... Common difference a = 28 - 1 9 = 9 First term = 19 a + b = 19 b = 19 - 9 = 10 n = 25 Sum = 1/2 an(n + 1) + nb = 1/2 x 9 x 25 x 26 + 25 x 10 = 3175 First term = 1 a + b = 1 b = 1 - 5 = -4 n = 25 Sum = 1/2 an (n + 1) + nb = 1/2 x 5 x 25 x 26 + 25 x -4 = 1525 |
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