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Question
Find the 31st term of an A.P. whose 11th term is 38 and the 16th term is 73.
Solution
Given that,
a11 = 38
a16 = 73
We know that,
an = a + (n − 1) d
a11 = a + (11 − 1) d
38 = a + 10d ...(1)
Similarly,
a16 = a + (16 − 1) d
73 = a + 15d ...(2)
On subtracting (1) from (2), we obtain
35 = 5d
d = 7
From equation (1),
38 = a + 10 × (7)
38 − 70 = a
a = −32
a31 = a + (31 − 1) d
= −32 + 30 (7)
= −32 + 210
= 178
Hence, 31st term is 178.
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