Sequences

Since, a,b and c are in an AP.
Let

%5Chspace%7B40mm%7D%20a%20%3DA%20-%20D%2C%20b%3D%20A%2C%20c%20%3D%20A%2BD

Given,

%5Chspace%7B20mm%7D%20a%20%2B%20b%20%2B%20c%20%3D%20%5Cfrac%7B3%7D%7B2%7D

%5CRightarrow%20%5C%2C%20%5C%2C%20(A%20-D)%20%2B%20A%20%2B%20(A%20%2B%20D)%20%3D%5Cfrac%7B3%7D%7B2%7D

%5CRightarrow%20%5Chspace%7B35mm%7D%203A%20%3D%5Cfrac%7B3%7D%7B2%7D%20%5C%2C%20%5C%2C%20%5CRightarrow%20%5C%2C%20%5C%2C%20%5C%2C%20A%20%3D%5Cfrac%7B1%7D%7B2%7D

%5Ctherefore

The number are

%5Cfrac%7B1%7D%7B2%7D%20-D%2C%5Cfrac%7B1%7D%7B2%7D%2C%5Cfrac%7B1%7D%7B2%7D%2BD.

Also,

%5Cbigg(%5Cfrac%7B1%7D%7B2%7D-D%5Cbigg)%5E2%2C%20%5Cfrac%7B1%7D%7B4%7D%2C%20%5Cbigg(%5Cfrac%7B1%7D%7B2%7D-D%5Cbigg)%5E2

are in Gp.

%5Ctherefore

%5Chspace%7B25mm%7D%20%5Cbigg(%5Cfrac%7B1%7D%7B4%7D%5Cbigg)%5E2%20%3D%20%5Cbigg(%5Cfrac%7B1%7D%7B2%7D-D%5Cbigg)%5E2%5C%2C%20%5Cbigg(%5Cfrac%7B1%7D%7B2%7D%2BD%5Cbigg)%5E2

%5CRightarrow%20%5Chspace%7B30mm%7D%20%5Cfrac%7B1%7D%7B16%7D%20%3D%20%5Cbigg(%5Cfrac%7B1%7D%7B4%7D-D%5E2%5Cbigg)%5E2%5C%2C

%5CRightarrow%20%5Chspace%7B22mm%7D%20%5Cfrac%7B1%7D%7B4%7D%20-D%5E2%20%3D%20%5Cpm%20%5Cfrac%7B1%7D%7B4%7D

%5CRightarrow%20%5Chspace%7B30mm%7D%20D%5E2%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5CRightarrow%20D%20%3D%20%5Cpm%20%5Cfrac%7B1%7D%7B%5Csqrt%202%7D

%5Ctherefore

%5Chspace%7B30mm%7D%20a%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Cpm%20%5Cfrac%7B1%7D%7B%5Csqrt%202%7D

So, out of the given values,

a%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20-%20%5Cfrac%7B1%7D%7B%5Csqrt%202%7D

is the right choice.

Chapter Questions
1 MCQs