find the number of terms in the A.P. 3,7,11,........407.Also find 20th term from the end

3,7,11,.................,407

407= 3+(n-1)(4)    nth term = a+(n-1)d

 = 3+4n-4

 = 4n-1

 408=4n

n=408/4

n=102

Number of terms = 102

It we start from last

Then first term =407

common difference =(-4)

20th term = 407 + (20-1) (-4)

 = 407+ 19 * (-4)

 = 407 - 76  

     = 331 ans.

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