What is d?

Algebra Level 1

In an arithmetic sequence, the sixth term is twice the third term and the 30th term is 60. Find the common difference


The answer is 2.

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1 solution

Syed Baqir
Sep 19, 2015

a 6 = 2 a 3 a + 5 d = 2 ( a + 2 d ) a + 5 d = 21 + 4 d 0 = a d a = d a_{6} = 2*a_{3} \rightarrow a + 5d = 2 ( a + 2d ) \\ a + 5d = 21 + 4d \\ 0 = a - d \\ \Rightarrow a = d \\

a 30 = 60 a + 29 d = 60 t h e r e f o r e : d + 29 d = 60 30 d = 60 d = 2 a_{30} = 60 \\ a + 29d = 60 \\ therefore: d + 29d = 60 \\ 30d = 60 \\ d = 2

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