Question

The first term of an



a.P is 5.The last term is 45 and the s of all its terms is 400.Find the number of terms and the common difference of the



a.P

Answer 1

Hey mate,

a=5,an=45,sn=400

sn=n/2(a+an)

400=n/2(5+45)

400=n/2x50

400=25n

n=16,number of terms=16

an=a+(n-1)d

45=5+(16-1)d

40=15d

d=2.67

Answer 2

Given:

First Term of the AP (a) = 5

Last Term of the AP (l) = 45

The sum of all terms of the ap (sn) = 400

The Formula used to find the sum of n terms of an AP:

Sn = n/2 (2a + (n - 1))

Calculating:

Substituting the values into this formula we get:

400 = n/2 (5 + 45)

400 x 2 = n (5 + 45)

800 = 50 n

n = 800 / 50

n = 16

Therefore, the n the term of ap is 16.

Now Finding the common difference of the AP:

Given the 16 th term is 45

a + 15 d = 45

Substituting the values into this formula we get:

5 + 15 d = 45

15 d = 40

d = 40 / 15

d = 8 / 3

Therefore, the common difference of the ap is 8/3.