Question

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.

Answer 1

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

∴ First term =a=t₁= 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)`

∴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 15^th term of this A.P. is 138.