Finite arithmetic sequence

How many numbers should be inserted between the numbers 1 and 25 so that all numbers create a finite arithmetic sequence and that the sum of all members of this group is 117?

Correct answer:

n =  7

Step-by-step explanation:

x (1+25)/2=117  26x=234  x=9  n=x2=92=7   Verifying Solution:  a1=1 a9=25 d=a9a1n+1=2517+1=3 a2=a1+d=1+3=4 a3=a2+d=4+3=7 a4=a3+d=7+3=10 a5=a4+d=10+3=13 a6=a5+d=13+3=16 a7=a6+d=16+3=19 a8=a7+d=19+3=22   Verifying Solution:  b9=a8+d=22+3=25 b9=a9

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