# find the sum of the following series 10 + 14 + 18 + 22 + ................ + 104

_{n}= 102 :

We have, a = 10, d = 14 - 10 = 4, a

_{n}= 102

a

_{n}= a + (n - 1)d

=> 102 = 10 + (n - 1)4

=> 102 = 10 + 4n - 4

=> 102 = 4n + 6

=> 4n = 96

=> n = 96/4 = 24

S

_{n}= n/2 [2a + (n - 1)d]

=> S

_{24}= 24/2 [2(10) + (24 - 1)4]

=> S

_{24}= 12 (20 + 92)

=> S

_{24}= 12 * 112 = 1344

Thus, the sum of the given list of numbers is 1344 when a

_{n}= 102

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