Question

what is 5, 9, 13, ..., 101?

Answer 1

Answer:

Step-by-step explanation: This is a finite arithmetic progression because the common different (d)=9-5

=4

Similarly for next terms it is also, 4 i.e (13-9)=4. Why finite A.P? Reason is that the last term i.e, 101 is known to us.

Answer 2

Finite AP with 25 terms

Step-by-step explanation:

5, 9, 13, ..., 101 is an arithmetic progression.

First term = a = 5

Last term = l = a + (n – 1) d = 101

Common difference d = +4

The arithmetic progression is finite as we know the end of the AP.

a + (n-1)d = 101

5 + (n-1)4 = 101

 5 + 4n - 4 = 101

 4n = 100

 n = 25

Sum of AP = n/2 [ 2a + (n-1)d]

S = n/2 [ a + a +(n-1)d] = n/2 ( a + l)

   = 25 / 2 ( 5 + 101)

    = 25 * 53

S = 1325