Question

Insert seven numbers between the two numbers 12 and 196 such that the nine numbers form an arithmetic sequence.

Find the common difference of the sequence.

Write down the sequence formed.

Collected in the board: Arithmetic sequence

Steven Zheng posted 2 months ago


Answer

Using the formula for general terms of an arithmetic sequence

a_1= 12

a_9=a_1+8d = 196

d=\dfrac{196-12}{8} =23

a_2= a_1+d = 12+23=35

a_3= a_1+2d = 12+2\times 23 =58

a_4= a_1+3d=12+3\times 23 =81

a_5= a_1+4d = 12+4\times 23 = 104

a_6= a_1+5d=12+5\times 23 = 127

a_7= a_1+6d=12+6\times 23=150

a_8= a_1+7d=12+7\times 23=173

Now the sequence formed is

12,35,58,81,104,127,150,173,196

Steven Zheng posted 1 month ago

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