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}Â term, a_{11}Â = 38and 16

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

a

_{n}Â =Â a+(nâˆ’1)da

_{11}Â =Â a+(11âˆ’1)d38 =Â a+10dÂ â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦.Â

(i)In the same way,

a_{16}Â =ÂaÂ +(16âˆ’1)d73 =Â

a+15dÂ â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦Â(ii)On subtracting equation

Â (i)Â fromÂ (ii), we get35 = 5

ddÂ = 7From equationÂ

(i), we can write,38 =Â

a+10Ã—(7)38 âˆ’ 70 =Â a

aÂ = âˆ’32

a

_{31}Â =Â aÂ +(31âˆ’1)Â d= âˆ’ 32 + 30 (7)

= âˆ’ 32 + 210

= 178

Hence, 31

^{st}Â term is 178.