The first three and last terms of an arithmetic sequence are $$7,13,19,\dots,1357$$

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Uniteasy Admin · Accepted Answer

(1) The common difference d is,
$$13-7=6$$
(2) Using the formula for general terms of an arithmetic sequence, 
$$
a_1=7$$, $$a_n=1357$$, $$d=6$$ 
$$a_n=a_1+(n-1)d$$
$$ n=\dfrac{a_n-a_1}{d}+1=\dfrac{1357-7}{6}=225 $$
(3) The sum of sequence from the 1st and 225th terms is,
$$S_{225}=\dfrac{225(a_1+a_{225})}{2}=\dfrac{225(7+1357)}{2}=153450 $$

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