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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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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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1. Solution:

(i)Â Given,

First term,Â aÂ = 7

Common difference,Â dÂ = 3

Number of terms,Â nÂ = 8,

We have to find the nth term,Â anÂ = ?

For an A.P,

anÂ =Â a+(nâˆ’1)d

Putting Down the values,

7+(8 âˆ’1) 3

7+(7) 3

7+21 = 28

anÂ = 28

(ii)

a = -18

dÂ = ?

nÂ = 10

anÂ = 0

For a A.P we use:-

anÂ =Â a+(nâˆ’1)d

Putting Down the values,

0 = âˆ’ 18 +(10âˆ’1)d

18 = 9d

dÂ = 18/9 = 2

So, c.d or dÂ = 2

(iii)

aÂ = ?

dÂ = -3

nÂ = 18

anÂ = -5

We know for an A.P.,

anÂ =Â a+(nâˆ’1)d

Putting down 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

aÂ = 46

(iv) It is Given That,

aÂ = -18.9

dÂ = 2.5

nÂ = ?

anÂ = 3.6

We know for A.P:-

anÂ =Â aÂ +(nÂ âˆ’1)d

Putting down 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) It isÂ Given,

aÂ = 3.5

dÂ = 0

nÂ = 105

nth term , anÂ = ?

For an A.P we know:

anÂ =Â a+(nÂ âˆ’1)d

Putting down the values,

anÂ = 3.5+(105âˆ’1) 0

anÂ = 3.5+104Ã—0

anÂ = 3.5

So, anÂ = 3.5

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