If the sum of 6 terms of an A.P. is 57 and the sum of its 10 terms is 155 , find the 25th term .
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S6 = 57
S10 =155
S6 = n/2[a + (n-1)d]
57 = 6/2[a + (6-1)d]
57 = 3[a + 5d]
57/3 = a + 5d
19 = a + 5d
a + 5d = 19
S10 = 155
S10 = n/2[a + (n-1)d]
155 = 10/2[a + (10-1)d]
155 = 5[a + 9d]
155/5 = a + 9d
31 = a + 9d
a + 9d = 31
a + 5d = 19
a + 9d = 31 -
__________
- 4d = -12
4d = 12
d = 12/4 = 3
a + 5d = 19
a + 5 × 3 = 19
a + 15 = 19
a = 19 - 15
a = 4
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