Answer:
Third term is 67.
Step-by-step explanation:
Let the first term of the sequence be [tex]x[/tex].
Given:
The second term is 5 more than the first term.
Second term = [tex]x+5[/tex]
Third term = First term + Second term = [tex]x+x+5=2x+5[/tex]
Fourth term = Second term + Third term = [tex]x+5+2x+5=3x+10[/tex]
Sum of first 4 terms is 237. Therefore,
[tex]x+(x+5)+(2x+5)+(3x+10)=237\\(x+x+2x+3x) + (5+5+10)=237.........(\textrm{Commutative property of addition})\\7x+20=237\\7x=237-20\\7x=217\\x=\frac{217}{7}=31[/tex]
Now, the third term of the sequence is given as:
[tex]\textrm{Third term}=2x+5=2(31)+5=62+5=67[/tex]
