This question is from Ncert Book class 10th Chapter no.5 Ex. 5.2 Question 1. In the following question you have fill all of the blanks given in the above picture. Give the solution one by one.

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# Fill in the blanks in the given table. It is given that ‘ a ‘ is the first term & ‘ d ‘ is the common difference and an the n th term of the A.P.

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Solution:(i)ÂGiven,First term,Â

aÂ = 7Common difference,Â

dÂ = 3Number of terms,Â

nÂ = 8,We have to find the nth term,Â

aÂ = ?_{n}For an A.P,

aÂ =Â_{n}a+(nâˆ’1)dPutting Down the values,

7+(8 âˆ’1) 3

7+(7) 3

7+21 = 28

aÂ = 28_{n}(ii)a= -18dÂ = ?nÂ = 10aÂ = 0_{n}For a A.P we use:-

aÂ =Â_{n}a+(nâˆ’1)dPutting Down the values,

0 = âˆ’ 18 +(10âˆ’1)

d18 = 9

ddÂ = 18/9 = 2So, c.d or

dÂ= 2(iii)aÂ = ?dÂ = -3nÂ = 18aÂ = -5_{n}We know for an A.P.,

aÂ =Â_{n}a+(nâˆ’1)dPutting down the values,

âˆ’5 =Â

a+(18âˆ’1) (âˆ’3)âˆ’5 =Â

a+(17) (âˆ’3)âˆ’5 =Â

aâˆ’51aÂ = 51âˆ’5 = 46aÂ = 46(iv)It is Given That,aÂ = -18.9dÂ = 2.5nÂ = ?aÂ = 3.6_{n}We know for A.P:-

aÂ =Â_{n}aÂ +(nÂ âˆ’1)dPutting down the values:

3.6 = âˆ’ 18.9+(

nÂ âˆ’1)2.53.6 + 18.9 = (

nâˆ’1)2.522.5 = (

nâˆ’1)2.5(

nÂ â€“ 1) = 22.5/2.5nÂ â€“ 1 = 9nÂ = 10Hence,Â

nÂ = 10(v)It isÂ Given,aÂ = 3.5dÂ = 0nÂ = 105nth term ,

aÂ = ?_{n}For an A.P we know:

aÂ =Â_{n}a+(nÂ âˆ’1)dPutting down the values,

aÂ = 3.5+(105âˆ’1) 0_{n}aÂ = 3.5+104Ã—0_{n}aÂ = 3.5_{n}So, aÂ = 3.5_{n}