An important question from ML Agarwal of Class10
Find the 31st term of an AP whose 11th term is 38 and 16th term is 73.
Arithmetic Progression, ML Agarwal (avichal publication) chapter9, question no. 14
Find the 31st term of an AP whose 11th term is 38 and 16th term is 73.
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Given that, a11​=38  a16​=73
We know that,
an​=a+(n−1)d
a11​=a+(11−1)d
38=a+10d … (i)
Similarly,
a16​=a+(16−1)d
73=a+15d … (ii)
On subtracting (i) from (ii), we get
35=5d
∴d=7
From equation (i),
38=a+(10)(7)
⇒38−70=a
∴a=−32
Now a31​=a+(31−1)d
=−32+30(7)
=−32+210
=178
Hence, 31st  term is 178.