Arithmetic sequences and series

May 2010
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0
i have no idea how to even attempt a question like this....

Use the two given terms to find a, d, and tn for each arithmetic sequence

t5= 16 , t8=25

the answer should be a=4, d=3, tn=3n+1

help?
 

Prove It

MHF Helper
Aug 2008
12,883
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i have no idea how to even attempt a question like this....

Use the two given terms to find a, d, and tn for each arithmetic sequence

t5= 16 , t8=25

the answer should be a=4, d=3, tn=3n+1

help?
\(\displaystyle t_8 = t_5 + 3d\)

\(\displaystyle 25 = 16 + 3d\)

\(\displaystyle 9 = 3d\)

\(\displaystyle d = 3\).


\(\displaystyle a = t_1 = t_5 - 4d\)

\(\displaystyle = 16 - 4(3)\)

\(\displaystyle = 4\).


Since \(\displaystyle t_n = a + (n - 1)d\)

\(\displaystyle t_n = 4 + (n - 1)3\)

\(\displaystyle t_n = 4 + 3n - 3\)

\(\displaystyle t_n = 3n + 1\).
 
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