Question

What is the 25th term of the arithmetic sequence 2, 1 and 3 over 5, 1 and 1 over 5 ...?

Answer 1

is it \[(a _{n})=2,1,........\]and\[(b _{n})=\frac{ 3 }{ 5 },\frac{ 1 }{ 5 },........\]?

Answer 2

no, its \[(a _{n})=2, 1\frac{ 3 }{ 5 }, 1\frac{ 1 }{ 5 }...\]

Answer 3

\[(a _{n})=\frac{ 10 }{ 5 },\frac{ 8 }{ 5 },\frac{ 6 }{ 5 },........\]
common difference\[d=a _{2}-a _{1}=\frac{ 8 }{ 5 }-\frac{ 10 }{ 5 }=-\frac{ 2 }{ 5 }\]
use formula\[a _{n}=a _{1}+(n-1)d\]
\[a _{25}=a _{1}+24(-\frac{ 2 }{ 5 })=\frac{ 10 }{ 5 }-\frac{ 48 }{ 5 }=-\frac{ 38 }{ 5 }\]

Answer 4

Thanks! Now I can solve the rest of the test.