If the sum of three consecutive terms of an increasing A.P. is 51 and ...
Any quadratic eqn which has two roots say a,b...can b written as x^2-(a+b)x+ab...if we observe a+b=5i...is satisfied by frst option but...product is -6...so can u kindly check the que..i think it is wrong...que would b x^2-5i-6=0...then 1st option is crct or else none of the options is crct...
If the sum of three consecutive terms of an increasing A.P. is 51 and ...
Sum of three consecutive terms of an AP
Let the three consecutive terms be (a - d), a, and (a + d), where a is the second term and d is the common difference.
Given that the sum of these three terms is 51, we can write the equation as:
(a - d) + a + (a + d) = 51
Simplifying the equation, we get:
3a = 51
Dividing both sides by 3, we find:
a = 17
Product of first and third terms
The product of the first and third terms is 273. Using the same notation as before, we can write the equation as:
(a - d)(a + d) = 273
Substituting the value of a, we have:
(17 - d)(17 + d) = 273
Expanding the equation, we get:
289 - d^2 = 273
Rearranging the equation, we find:
d^2 = 289 - 273
d^2 = 16
Taking the square root of both sides, we have:
d = ±4
Since we are considering an increasing arithmetic progression, the common difference (d) must be positive. Therefore, d = 4.
Finding the third term
The third term can be found by adding the common difference (d) to the second term (a):
Third term = a + d
Third term = 17 + 4
Third term = 21
Therefore, the third term of the arithmetic progression is 21, which corresponds to option C.