Question

Find the indicated term of each arithmetic sequence a(1)=14, d=9, n=11

Answer 1

The first term of an arithmetic sequence is 14, that is:


`a_1=14`. Also, we are given that the common difference is 9, which means that each next term is obtained by adding 9, as follows:


`a_1=14\\\\a_2=14+9\\\\a_3=(14+9)+9\\\\a_4=(14+9+9)+9\\\\...`.


So we notice that to get the value of the n'th term,
`a_n`, we must add (n-1) nines to 14.

(For example, to find the second term we added 1 nine to 14. To find the third term we added 2 nines to 14, and so on...)

Thus,
`a_(11)=14+9 \cdot 10=14+90=104.`



Answer: 104.