Question

find the 31st term of an ap whose 11th term is 38 and the 16th term is 72
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Answer 1

Step-by-step explanation:

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.