The ratio of the product of the 1^st and the 4^th term of an AP to that of the 2^nd and the 3^rd term is 2:3. What is the common difference of this AP if the sum of all the 4 terms is 20?

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Solution

The correct option is D 2
The above terms are considered for easy calculation, terms can also be considered as a, a+d, a+2d..etc
Adding 4a= 20 a=5
Also given that $\frac{(5 - 3 d) \cdot (5 + 3 d)}{(5 - d) \cdot (5 + d)} = \frac{2}{3}$

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The ratio of the product of the 1st and the 4th term of an AP to that of the 2nd and the 3rd term is 2:3. What is the common difference of this AP if the sum of all the 4 terms is 20?

The correct option is D 2The above terms are considered for easy calculation, terms can also be considered as a, a+d, a+2d..etcAdding 4a= 20 a=5Also given that (5−3d)⋅(5+3d)(5−d)⋅(5+d)=23

The ratio of the product of the 1^st and the 4^th term of an AP to that of the 2^nd and the 3^rd term is 2:3. What is the common difference of this AP if the sum of all the 4 terms is 20?

The correct option is D 2
The above terms are considered for easy calculation, terms can also be considered as a, a+d, a+2d..etc
Adding 4a= 20 a=5
Also given that $\frac{(5 - 3 d) \cdot (5 + 3 d)}{(5 - d) \cdot (5 + d)} = \frac{2}{3}$