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Question

Question 7
Find the
31st term of an A.P. whose 11th term is 38 and the 16th term is 73.

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Solution

Given that, a11=38 and a16=73
We know that, an=a+(n1)d
a11=a+(111)d
38==a+10d ...(1)
Similarly, a16=a+(161)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+(311)d
=32+30(7)
=32+210
=178
Hence, 31st term is 178.


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