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

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)

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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

Posted by

Gautam harsolia

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