1.

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,….

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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