Question

how many terms of the a.p 24,2 1,18 must be taken so that their sum is 78

Answer 1

Answer:

n= 13 and 4

Step-by-step explanation:

AP: 24,21,18,......

Common Difference(d) = 21-24 = -3

First term(a) = 24

Sum of an a.p.(s)= 78              (given)

but, S=n/2[2a + (n-1)d]

Therefore, n/2[2a+(n-1)d] = 78

                  n[48+(n-1)(-3)] = 156

                  48n-3n^2+3n = 156

                  17n-n^2-52=0

                  n^2-17n+52=0

                  (n-13)(n-4)=0  => n=13 or 4

Answer 2

AP= 24,21,18
Sn = n/2(2a+(n-1)d)
78= n/2(2*24+(n-1)-3)
78*2 = n(48-3n^2+3n)
156= 48-3n^2+3n
3n^2-5n-156=0
then factorize by using splitting the middle term