Question

41. Divide 12.50 into five parts in A.P. such that the first part and the last part are in the ratio of 2:3​

Answer 1

Answer:

If first part = 2x,

fifth part = 3x

So, AP = 2x, 2x+d, 2x+ 2d, 2x+3d, 3x ( d is common difference)

The sum of these terms = 11x + 6d = 12.5 ……. (1)

5th term = T5 = 2x + 4d = 3x

=> x = 4d

By putting the value of x in (1)

11 * 4d + 6d = 12.5

=> 50d = 12.5

=> d= 1/4 = 0.25

Since, x = 4d

=> x= 4*(1/4) = 1

So, 5 parts are …..

,AP = 2, 2.25, 2.5, 2.75, 3

Step-by-step explanation:

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Answer 2

Answer:

If first part /5 th part=2:3

So, AP = 2x, 2x+d, 2x+ 2d, 2x+3d, 3x

The sum of these terms = 11x+ 6d = 12.5b. (eqn 1)

5th term = T5 = 2x + 4d = 3x

=> x = 4d

By putting the value of x in (1)

11×4d + 6d = 12.5

=> 50d =12.5

=> d = 12.5/50

d=0.25

Since, x = 4d

=4 ×0.25

=1.00

So, 5 parts are .....

AP = 2,. 2.25, 2.5, 2.75, 3