Question

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.

Collected in the board: Arithmetic sequence

Steven Zheng posted 2 months ago


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

Steven Zheng posted 2 months ago

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