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(1) Find the sum of the first 25 terms of each of the arithmetic sequences below 1 11, 22, 33, 12, 23, 34, ... in 21, 32, 43, ... iv) 19, 28, 37, ... v) 1, 6, 11, ... (2) What is the difference between the sum of the first 20 terms and the next 20 terms of the arithmetic sequence 6, 10, 14, ...? (3) Calculate the difference between the sums of the first 20 terms of the arithmetic sequences 6, 10, 14, ... and 15, 19, 23,... (4) Find the sum of all three digit numbers, which are multiples of 9. (5) The expressions for the sum to n terms of some arithmetic sequences u Gind the expression for the nth term of each:​

Answer :

anshurao496

Step-by-step explanation:

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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