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Question
Find the sum of all numbers from 50 to 350 which are divisible by 6. Hence find the 15th term of that A.P.
Solution
The numbers from 50 to 350 which are divisible by 6 are 54, 60, 66, ……, 348.
∴ First term =a=t1= 54, d= 6 and tn= 348
tn = 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)`
∴S50= `50/2(54+348)`
=25*402
=10050
t15 = 54+14(6)= 54+84 = 138
Thus, the sum of all numbers from 50 to 350,which are divisible by6, is 10050 and the 15th term of this A.P. is 138.
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