Question
Find the 31st term of an AP whose 11th term is 38 and 16th term is 73.
Answer: Option B
:
B
Given that
a11=38and a16=73,
wherea11is the 11th term anda16is the 16th term of an AP.
The nth term of an AP with first term a and common difference d is given by
an=a+(n−1)d.
⇒38=a+10d....(i)
73=a+15d....(ii)
Subtracting equation (i) from equation (ii), we get
35=5d.
⇒d=7
Substituting the value of d in equation (i), we get
a=38−10d=38−10(7)=−32.
Now, a31=a+(31−1)d=−32+30(7)
=178
Therefore, the 31st term of the given AP is 178.
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:
B
Given that
a11=38and a16=73,
wherea11is the 11th term anda16is the 16th term of an AP.
The nth term of an AP with first term a and common difference d is given by
an=a+(n−1)d.
⇒38=a+10d....(i)
73=a+15d....(ii)
Subtracting equation (i) from equation (ii), we get
35=5d.
⇒d=7
Substituting the value of d in equation (i), we get
a=38−10d=38−10(7)=−32.
Now, a31=a+(31−1)d=−32+30(7)
=178
Therefore, the 31st term of the given AP is 178.
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