Find the sum of all numbers from 50 to 350 which are divisible by 6. Hence find the 15^{th} term of that A.P.

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#### Solution

The numbers from 50 to 350 which are divisible by 6 are 54, 60, 66, ……, 348.

∴ First term =a=t_{1}= 54, d= 6 and t_{n}= 348

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

∴348 = 54+(n-1)6

∴294 = (n-1)6

∴49 = n-1

∴n = 50

`S_n= n/2(t_1+t_n)`

∴S_{50}= `50/2(54+348)`

=25*402

=10050

t_{15} = 54+14(6)= 54+84 = 138

Thus, the sum of all numbers from 50 to 350,which are divisible by6, is 10050 and the 15^{th} term of this A.P. is 138.

Concept: Sum of First n Terms of an AP

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