Arithmetic progression

Question

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

Answer 1

54 is ÷ by 6 (because it's digit-sum, 9, is divisible by 3 & 54 is even, too).

 

Successive numbers are obtained by addition of 6: 54, 60, 66, 72, 78, 84, 90, ...,348.

 

This arithmetic sequence has nth term 54 + 6(n-1) = 54 + 6(14) = 138.

Answer 2

54 is the first number divisible by 6.

348 is the last number divisible by 6.

 

348 = 54 + (n - 1)6

348 = 54 + 6n - 6

348 = 48 + 6n

300 = 6n

50 = n

 

S₅₀ = (50/2)(43 + 348)

S₅₀ = 25(391)

S₅₀ = 9775

 

I do no know what the 15th term has to do with the sum.