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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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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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1. (i)Â Given,

First term, aÂ = 7

Common difference,Â dÂ = 3

Number of terms,Â nÂ = 8,

We have to find the nth term, anÂ = ?

As we know, for an A.P.,

anÂ =Â a+(nâˆ’1)d

Putting the values,

=> 7+(8 âˆ’1) 3

=> 7+(7) 3

=> 7+21 = 28

Hence,Â anÂ = 28

(ii) Given,

First term, aÂ = -18

Common difference,Â dÂ = ?

Number of terms,Â nÂ = 10

Nth term, anÂ = 0

As we know, for an A.P.,

anÂ =Â a+(nâˆ’1)d

Putting the values,

0 = âˆ’ 18 +(10âˆ’1)d

18 = 9d

dÂ = 18/9 = 2

Hence, common difference,Â dÂ = 2

(iii) Given,

First term, aÂ = ?

Common difference,Â dÂ = -3

Number of terms,Â nÂ = 18

Nth term, anÂ = -5

As we know, for an A.P.,

anÂ =Â a+(nâˆ’1)d

Putting the values,

âˆ’5 =Â a+(18âˆ’1) (âˆ’3)

âˆ’5 =Â a+(17) (âˆ’3)

âˆ’5 =Â aâˆ’51

aÂ = 51âˆ’5 = 46

Hence,Â aÂ = 46

(iv)Â Given,

First term, aÂ = -18.9

Common difference,Â dÂ = 2.5

Number of terms,Â nÂ = ?

Nth term, anÂ = 3.6

As we know, for an A.P.,

anÂ =Â aÂ +(nÂ âˆ’1)d

Putting the values,

3.6 = âˆ’ 18.9+(nÂ âˆ’1)2.5

3.6 + 18.9 = (nâˆ’1)2.5

22.5 = (nâˆ’1)2.5

(nÂ â€“ 1) = 22.5/2.5

nÂ â€“ 1 = 9

nÂ = 10

Hence,Â nÂ = 10

(v)Â Given,

First term, aÂ = 3.5

Common difference,Â dÂ = 0

Number of terms,Â nÂ = 105

Nth term, anÂ = ?

As we know, for an A.P.,

anÂ =Â a+(nÂ âˆ’1)d

Putting the values,

anÂ = 3.5+(105âˆ’1) 0

anÂ = 3.5+104Ã—0

anÂ = 3.5

Hence,Â anÂ = 3.5

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