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Question
Find the sum of all numbers from 50 to 350 which are divisible by 4. Also, find the 15th term.
Solution
The numbers from 50 to 350 which are divisible by 4 are
52, 56 , 60, .... 348
It is an A.P. where a = 52 and d = 4
Let tn = 348
tn = a+ (n-1)d
∴ 348 = 52 + (n - 1)(4)
348 - 52 = 4 (n - 1)
`296/4 = "n" -1`
∴ n = 74 + 1
∴ n = 75
`"S"_"n" = "n"/2["t"_1 + "t"_"n"]`
`"S"_25 =25/2 [52 + 348]`
`= 25/2 xx 400`
`"S"_25 = 5000`
∴ The sum of all numbers from 50 to 350 which are divisible by 4 is 5000.
tn = a + (n - 1)d
∴ t15 = 52 + (15 - 1)(4)
= 52 + 14(4)
= 52 + 56
= 108
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