Q : 7       Find the  \small 31st term of an AP whose \small 11th term is \small 38 and the \small 16th term is \small 73.

Answers (1)

It is given that
 \small 11th term of an AP is  \small 38 and the \small 16th term is \small 73
Now,
a_{11} =38= a+ 10d \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ -(i)
And
a_{16} =73= a+ 15d \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ -(ii)
On solving equation (i) and (ii) we will get 
a= -32 \ \ \ and \ \ \ d = 7
Now,
a_{31} = a+30d = -32 + 30\times 7 = -32+210 = 178
Therefore, 31st terms of given AP is 178

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