In an arithmetic sequence, the sixth term is twice the third term and the 30th term is 60. Find the common difference
+128407 60 = a + d (30-1)
60 = a + 29d ⇒ a = 60 -29d (1)
3rd term = a + 2d
The sixth term = a + 5d
And we know that
2(a + 2d) = a + 5d sub (1) into this
2 ( 60 - 29d + 2d) = 60 - 29d + 5d
2 ( 60 - 27d) = 60 - 24d
120 - 54d = 60 - 24d
120 - 60 = 54d - 24d
60 = 30d
d = 60 / 30 = 2
