How i solve the question of arithmetic progressions of ncert of class 10th How i solve the class 10th question of exercise 5.2 Fill in the blanks in the following table, given that a is the first term, d the common difference and an the nth term of the A.P.

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# Fill in the blanks in the following table, given that a is the first term, d the common difference and an the nth term of the A.P. Q.1

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(i)ÂGiven,First term,

aÂ = 7Common difference,Â

dÂ = 3Number of terms,Â

nÂ = 8,We have to find the nth term,

aÂ = ?_{n}As we know, for an A.P.,

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

=> 7+(8 âˆ’1) 3

=> 7+(7) 3

=> 7+21 = 28

Hence,

Â aÂ = 28_{n}(ii)Given,First term,

aÂ = -18Common difference,Â

dÂ = ?Number of terms,Â

nÂ = 10Nth term,

aÂ = 0_{n}As we know, for an A.P.,

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

0 = âˆ’ 18 +(10âˆ’1)

d18 = 9

ddÂ = 18/9 = 2Hence, common difference,Â

dÂ= 2(iii)Given,First term,

aÂ = ?Common difference,Â

dÂ = -3Number of terms,Â

nÂ = 18Nth term,

aÂ = -5_{n}As we know, for an A.P.,

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

âˆ’5 =Â

a+(18âˆ’1) (âˆ’3)âˆ’5 =Â

a+(17) (âˆ’3)âˆ’5 =Â

aâˆ’51aÂ = 51âˆ’5 = 46Hence,Â

aÂ = 46(iv)Â Given,First term,

aÂ = -18.9Common difference,Â

dÂ = 2.5Number of terms,Â

nÂ = ?Nth term,

aÂ = 3.6_{n}As we know, for an A.P.,

aÂ =Â_{n}aÂ +(nÂ âˆ’1)dPutting 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)Â Given,First term,

aÂ = 3.5Common difference,Â

dÂ = 0Number of terms,Â

nÂ = 105Nth term,

aÂ = ?_{n}As we know, for an A.P.,

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

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

aÂ = 3.5_{n}