In an A.P. if the 12th term is -13 and the sum of the first four terms is 24, what is the sum of the first 10 terms ?

Question

Plz solve it.

Answer 1

first four terms are a, a+d, a+2d, a+3d; total 4a + 6d = 24

 

twelfth term is a + 11 d = -24

 

there you have two linear equations, two unknowns -- solve that system; then you can calculate the sum of n terms using the A.P. Series Sum formula.

Answer 2

For the 12th terms

-13 = a₁ + 11d

-13 - 11d = a₁

For the sum of four

24 = (4/2)(2(-13 - 11d) + 3d))

24 = 2(2(-13 - 11d + 3d)

12 = 2(-13 - 8d)

12 = -26 - 16d

38 = - 16d

 

Can you now determine the sum of ten terms?