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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.
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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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