Question

in an ap if the 12th term is the minus 13 and the sum of first four term is 24 what is the sum of the first 10 terms?




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Answer 1

t 12 = a + (12-1) d
= a + 11d = -13 ( given)
S4 = 4/2 {2a + (4-1)d}= 24
=2( 2a + 3d) = 24
= 4a + 6d = 24
Now, we have two equations and two variables,
So,
a+11d= -13
4a+6d= 24
Multiplying eq 1 by 4 we get,
4a + 44d = -52. .... 1
4a + 6d. = 24 ...... 2
Subracting eq 2 from 1 we get
38d = -76
d= -2
putting d = -2 in eq 1
4a - 82 = -52
4a = 30
a= 30/4
Sum of first 10 terms is:
2a + (n-1)d
15 + 9*(-2)
15-18
-3
a= 7.5