Example 4: Sapna's father planted 4 trees in his garden, when he was 22 years old. After that, every year he planted one more tree than the number of trees he planted in the previous year. How many trees will be there in his garden when he will become 40 years old?
 

Dear student,
Here is the solution of your asked query:
Let the number of trees be n when he will become 40 years old.Number of trees planted when his age was 22 years old= 4Now according to question we have;number of trees planted at an age of 23 =5number of trees planted at an age of 24 =6So here common difference d= 1first term, a=4number of terms, n= (40-22)+1=19So sum of n terms =S19=1922×4+19-1×1=192×26=247Therefore total number of trees at an age of 40 years = 247
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 be 225 trees in the garden
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I don't know its correct or not

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correct
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thankss
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A.P. for the age will be
22,23,24,.....
a=22
d=23-22=1
an=40
n=?
an=a+(n-1)d
40=22+(n-1)1
40-22=n-1
18+1=n
n=19
n is whole number so 40 years is 19thterm

now,A.P. for the number of plants will be
4,5,6,......
a=4
d=4-3=1
n=19
an=?

an=a+(n-1)d
an=4+(19-1)1
an=4+18
an=22

there will be 22 trees in the garden when he will become 22 years



 
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Acc to qn

AP:4,1+4,1+1+4,and so on
i.e,4,5,6,7,8 and so on

22nd year ,he planted 4: 23rd , he planted 5 and so on

So we should find how many trees were planted on the 40th year.

So (40-22)+1 will give the total number of years. 
So we should find a19 because 40-22 +1 =19
an=a+(n-1)d

a=4
n=19
d=1(5-4)
Substituting the values
a19=4+(19-1)1
a19=4+ 18 =>22


 therefore,22 trees will be planted on the 40th year.
                                                                          VERIFICATION
4 trees=22nd year, 5 trees=23rd year and when u do it in the same manner u will get  22 trees=40th year



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