How do you find the formula for #a_n# for the arithmetic sequence #a_5=190, a_10=115#?

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Answer 1 · 2017-02-13T22:17:37

See explanation.

From the given data we can easily calculate the difference #d# of the sequence.

If #a_5=a_1+4*d# and #a_10=a_1+9*d#, the we can calculate that:

#a_10-a_5=5*d#, so: #d=(a_10-a_5)/5#

#d=(115-190)/5=-75/5=-15#

Now we can calculate #a_1# using:

#a_5=a_1+4*d#

#190=a_1+4*(-15)#

#190=a_1-60#

#a_1=250#

So finally the #n-th# term is:

#a_n=250+(n-1)*(-15)#

#a_n=250-15n+15#

#a_n=-15n+265#