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.