In 1654 Blaise Pascal invented Pascal's triangle,for which the
first four rows are given:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
--1 6 15 20 15 6 1
--1 7 21 35 35 21 7 1
Determine the ratio of the sums of the terms of the seventh and
eighth rows.
Is this answer correct?
Seventh- 127
Eighth- 136
1
1 1
1 2 1
1 3 3 1
To determine the ratio of the sums of the terms in the seventh and eighth rows of Pascal's triangle, we first need to find the sums of the terms in each row.
To find the sum of the terms in a row of Pascal's triangle, we can use the formula for the sum of the terms in the nth row, which is 2^n. However, in this case, we have to subtract 1 from the formula since the first term is always 1.
For the seventh row:
Sum of terms = 2^7 - 1 = 128 - 1 = 127
For the eighth row:
Sum of terms = 2^8 - 1 = 256 - 1 = 255
So, the sum of the terms in the seventh row is 127 and the sum of the terms in the eighth row is 255.
Now, to find the ratio, we divide the sum of the terms in the seventh row by the sum of the terms in the eighth row:
Ratio = (Sum of seventh row) / (Sum of eighth row)
= 127 / 255
Simplifying the ratio, we get:
Ratio = 1 / 2
Therefore, the correct answer for the ratio of the sums of the terms in the seventh and eighth rows is 1/2, not 127/136.