The question is given from NCERT Book of class 10th Ch. no. 5 Ex. 5.2 Q. 7. In the following question you have to find the 31st term of an A.P whose 11th term is 38 & 16th term is 73. Give the answer briefly.

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Given that,

11

^{th}term, a_{11}= 38and 16

^{th}term, a_{16}= 73We know that,

a

_{n}= a+(n−1)da

_{11}= a+(11−1)d38 = a+10d ……………………………….

(i)In the same way,

a_{16}=a+(16−1)d73 =

a+15d…………………………………………(ii)On subtracting equation

(i)from(ii), we get35 = 5

dd= 7From equation

(i), we can write,38 =

a+10×(7)38 − 70 = a

a = −32

a

_{31}= a +(31−1) d= − 32 + 30 (7)

= − 32 + 210

= 178

Hence, 31

^{st}term is 178.