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Quantitative Aptitude Question on Co-ordinate Geometry

If the square of the 7th term of an arithmetic progression with positive common difference equals the product of the 3rd and 17th terms, then the ratio of the first term to the common difference is

A

2: 3

B

3 : 2

C

3: 4

D

4: 3

Answer

2: 3

Explanation

Solution

Let the first term be a and the common difference be d.
The given expression (a+6d)2=(a+2d)(a+16d)(a+6d)^2=(a+2d)(a+16d) can be expanded as follows:
a2+12ad+36d2=a2+18ad+32d2a^2+12ad+36d^2=a^2+18ad+32d^2

Simplifying the equation, we get:
4d2=6ad4d^2=6ad
⇒ad=23⇒\frac{ a}{d}=\frac{2}{3}