The figure below shows that the fourth triangular number, 10 , added to the fifth triangular number, 15 , produces the fifth square number, 25 . a. Use a drawing to show that the fifth triangular number added to the sixth triangular number is the sixth square number. b. Verify that the 50 th triangular number added to the 51 st triangular number is the 51 st square number. Hint: Use a numerical approach; don’t use a drawing. c. Use nth-term formulas to verify that the sum of the nth triangular number and the ( n + 1 ) s t triangular number is always the square number ( n + 1 ) 2 .
The figure below shows that the fourth triangular number, 10 , added to the fifth triangular number, 15 , produces the fifth square number, 25 . a. Use a drawing to show that the fifth triangular number added to the sixth triangular number is the sixth square number. b. Verify that the 50 th triangular number added to the 51 st triangular number is the 51 st square number. Hint: Use a numerical approach; don’t use a drawing. c. Use nth-term formulas to verify that the sum of the nth triangular number and the ( n + 1 ) s t triangular number is always the square number ( n + 1 ) 2 .
The figure below shows that the fourth triangular number,
10
, added to the fifth triangular number,
15
, produces the fifth square number,
25
.
a. Use a drawing to show that the fifth triangular number added to the sixth triangular number is the sixth square number.
b. Verify that the 50th triangular number added to the 51st triangular number is the 51st square number. Hint: Use a numerical approach; don’t use a drawing.
c. Use nth-term formulas to verify that the sum of the nth triangular number and the
(
n
+
1
)
s
t
triangular number is always the square number
(
n
+
1
)
2
.
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