Answer:
The explicit formula for Arithmetic Sequence is \(a_n=7.02+0.33n\)
Step-by-step explanation:
Given: Foot length & shoe size in AP.
\(a_n\) is foot length and n is shoe size.i.e., \(a_{12}=11\:and\:a_7=9.33\)
To find: Formula for Arithmetic sequence .i.e., \(a_n\)
From question,
\(a_{12}-a_7=11-9.33=1.67\)
Also, we know that
\(a_{12}=a_7+5d\\5d=a_{12}-a_7\\5d=1.67\\d=\frac{1.67}{5}\\\\d=0.33\)
Now, consider
\(a_7=a_1+6d\\a_7=a+6d\\a=a_7-6d\\a=9.33-6\times0.33\\a=9.33-1.98\\a=7.35\)
Thus using formula of \(a_n\) we get,
\(a_n=a+(n-1)d\\a_n=7.35+(n-1)\times0.33\\a_n=7.35+0.33n-0.33\\a_n=7.02+0.33n\)
Therefore, The explicit formula for Arithmetic Sequence is \(a_n=7.02+0.33n\)
