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Question

Find the 31st term of an AP whose 11th term is 38 and 16th term is 73.


A

150

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B

178

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C

210

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D

185

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Solution

The correct option is B

178


We are given that a11=38 and a16=73 where, a11 is the 11th term and a16 is the 16th term of an AP.

Using formula an=a+(n1)d, to find nth term of arithmetic progression, we get;
38=a+(111)d
73=a+(161)d
38=a+10d ....(1)
73=a+15d .....(2)
These are equations consisting of two variables. Let’s solve them using substitution method.
We have,
38=a+10d
a=3810d

Let’s put value of a in the equation (2), we get
73=3810d+15d
35=5d
Therefore Common difference is, d = 7.
Putting value of d in equation (1), we get
38=a+70
a=32
Therefore, common difference is d=7.
First term, a=32
Using formula an=a+(n1)d to find nth term of arithmetic progression, we get
a31=32+(311)(7) = −32+210 = 178
Therefore, 31st term of AP is 178.


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