find the 31st term of an ap whose 11th term is 38 and the 16th term is 73
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Answer:
Given that, a
11
=38 a
16
=73
We know that,
a
n
=a+(n−1)d
a
11
=a+(11−1)d
38=a+10d ... (i)
Similarly,
a
16
=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 a
31
=a+(31−1)d
=−32+30(7)
=−32+210
=178
Hence, 31
st
term is 178.
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