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

Question

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

Uniteasy Admin · Accepted Answer

Using the formula for general terms of an arithmetic sequence
$$a_1= 12$$
$$a_9=a_1+8d = 196$$
$$d=\dfrac{196-12}{8}  =23$$ $$a_2= a_1+d = 12+23=35$$
$$a_3= a_1+2d = 12+2	imes 23 =58 $$
$$a_4= a_1+3d=12+3	imes 23 =81$$
$$a_5= a_1+4d = 12+4	imes 23 = 104$$
$$a_6= a_1+5d=12+5	imes 23 = 127 $$
$$a_7= a_1+6d=12+6	imes  23=150$$
$$a_8= a_1+7d=12+7	imes 23=173 $$
Now the sequence formed is
$$12,35,58,81,104,127,150,173,196$$

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