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.
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.
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