Question

The sum of first six terms of AP is 42.The ratio of it's 10th term to it's 13 the term is1:3.calculate it's 1st and 3rd term.

Answer 1

Answer:

1st term =21/2

3rd term = 77/10

Step-by-step explanation:

Let the 6 terms of AP be a,a+d,a+2d,a+3d,a+4d,a+5d

Sum of the 6 terms:

a+a+d+a+2d+a+3d+a+4d+a+5d=42

6a+15d=42

2a+5d = 14 - eqn (1)

Now,

(a+9d)/(a+12d) = 1/3

Solving above question:

3(a+9d)=a+12d

3a+27d-a-12d=0

2a+15d=0

a=-(15/2)d

Now, from eqn (1), we have:

-2d(15/2)+5d=14

-15d+5d=14

-10d=14

Thus, d=-7/5

Therefore, a=21/2

1st term = a = 21/2

3rd term = a+2d = 21/2-2(7/5) = 77/10