Question

in an apthe 12 term is-13and the sum of first four term is 24 what is the sum of first 10 terms?

Answer 1

Let a and b are first term and 
common difference of an A P.
n th term = tn = a+ ( n - 1 ) d 
i) given t12 = - 13
a + 11d = -13 ---------(1)
ii) sum of first 4 terms = 24 
********************************************Sn = n/2 [ 2a + ( n-1 ) d ]*********************************************S4 = 24
4/2 [ 2a + 3d] = 24
2[2a + 3d ] = 24
2a + 3d = 12 ------------(2 )
Multiply equation ( 1 ) with 2 and
subtract from (2)
We get 
-19 d = 38
d = -2Put d value in (1)
a - 22 = -13
a = -13 + 22
a = 9
iii) a = 9 , d = -2 , n =10
S 10 = 10/2 [ 2 × 9 + ( 10 - 1 ) ( - 2 ) ]
= 5 [ 18 - 18 ]
= 5 × 0
= 0
Therefore,
Sum of first 10 terms = S 10 = 0
I hope this will useful to you.