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

Find the common difference.

Find the number of terms in the sequence.

What is the sum of the sequence.

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

Find the common difference.

Find the number of terms in the sequence.

What is the sum of the sequence.

(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