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Question
The 11th term and the 21st term of an A.P are 16 and 29 respectively, then find the first term, common difference and the 34th term.
Solution
t11 = 16 and t21 = 29
t1 = ?, d = ? and t34 = ?
tn = a + (n - 1) d
t11 = a + (11 - 1) d
16 = a + 10 d ......(1)
t21 = a + (21 - 1) d
29 = a + 20d .........(2)
Subtracting equation (1) and (2)
a + 20 d = 29
a + 10 d = 16
_________________
10 d = 13
d = `13/10`
d = 1.3
Substituting d = 1.3 in equation (1)
16 = a + 10 d
a + 10 (1.3) = 16
a + 13 = 16
a = 16 - 13
a = 3
t34 = 3 + (34 - 1) (1.3)
= 3 + 33(1.3)
= 3 + 42.9
t34 = 45.9
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