How do you write a rule for the nth term of the arithmetic sequence given #a_5=10#, #a_12=24#?

1 Answer
Aug 29, 2016

Answer:

#n^(th)# term #a_n=2n#

Explanation:

In an arithmetic sequence, if #a_1# is the first term and #d# is the difference between a term and its preceding term, than the #n^(th)# term #a_n# is given by #a_n=a_1+(n-1)d#.

Here, we have #a_5=a_1+4d=10# and #a_(12)=a_1+11d=24#. Subtracting former from latter equation, we get

#7d=14# or #d=14/7=2# and #a_1=10-4d=10-4×2=10-8=2#.

Hence, #a_n=a_1+(n-1)d#

= #2+(n-1)×2=2+2n-2=2n#