How do you find the formula for the arithmetic sequence where #a_4 = 10# and #a_10 = 28#?

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Answer 1 · 2017-03-17T06:37:35

#a_n=3n-2#

In an arithmetic sequence if #m^(th)# term is #a_m# and #n^(th)# term is #a_n#, then common difference #d# is given by

#d=(a_m-a_n)/(m-n)#

As we are given #a_4=10# and #a_10=28#,

#d=(28-10)/(10-4)=18/6=3#

Now if #a_1# is the first of arithmetic sequence and #d# is common difference, #n^(th)# term #a_n# is given by

#a_n=a_1+(n-1)d# and as #a_4=10#, we have #a_4=a_1+(4-1)xx3#

or #10=a_1+9# or #a_1=1#

and hence #a_n=1+(n-1)xx3=1+3n-3=3n-2#