Question

The first term of an A.P is 14 and the sum of the first five terms and the first ten

terms are equal in magnitude but opposite in sign. The 3rd term of the AP is:

Answer 1

Answer:70/11

Step-by-step explanation:

a=14

S(5) = -S(10)

5/2[2×14+(5-1)d] = -10/2[2×14+(10-1)d]

5[28+4d] = -10[28+9d]

10[14+2d] = -10[28+9d]

(14+2d) = -1(28+9d)

14+2d = -28-9d

-9d-2d = 14+28

-11d = 42

d = -42/11

now third term will be

a3 = a + 2d

     = 14 + 2(-42/11)

     = 14 - 84/11

     =(154 - 84)/11

     = 70/11