for a given ap the common difference is 5, and it's 15 th term is 72 .find the first term of an ap and its 50th term
Answers
Step-by-step explanation:
It is given that The 10th term of the AP is 65 and the 15th term is 80.
So, 80 = 65 + 5d; where 'd' is the common difference of the AP.
Solving the above renders 'd' as 3.
Now, we have to look for any integer term 'n' for which 200 = 65 + n×3.
Solving the above renders 'n' as 45.
So, 200 will be the 45th term if the FIRST term is 65.
But, we have 65 as the tenth term so there are 9 terms prior to 65.
So, 200 will be the value of the 45+9 = 54th term from the beginning of the series.
Answer:
Given : p(x) = x² + x - 12
To Find : zeroes of the quadratic polynomial
verify the relationship between the zeroes and the coefficients
Solution:
p(x) = x² + x - 12
x² + x - 12 = 0
=> x² + 4x - 3x - 12 = 0
=> x (x + 4) - 3(x + 4) = 0
=> (x - 3)(x + 4) = 0
Zeroes are 3 , - 4
Sum of zeroes = 3 - 4 = - 1
Product of zeroes = 3(-4) = - 12
ax² + bx + c = 0
product of zeroes = c/a
sum of zeroes = - b/a
comparing x² + x - 12 = 0 with ax² + bx + c = 0
a = 1 , b = 1 , c = - 12
product of zeroes = -12/1 = - 12
sum of zeroes = - 1/1 = - 1
relationship between the zeroes and the coefficients verified