Question

The first term of an ap is 9 the last term is 76 and the sum of all its term is 450 find the number of team and the common difference of the Ap

Answer 1

Your question needs a correction.

Correct value of last term = 66.

Answer:

the number of terms is 12 and the common difference between the terms is 5.

Step-by-step explanation:

It is given that the first term of an AP is 9 the last term is 76 and the sum of all its term is 450 .

Therefore,

a = first term = 9

l = last term = 66

S${}_{n}$ = 450

Let the number of terms in the progression be n,

From the properties of arithmetic progressions :

S${}_n = \dfrac{n}{2}[ a + l] \quad or \quad \dfrac{n}{2}[ 2a + ( n - 1 )d]$

Thus,

= > 450 = ( n / 2 ) [ 9 + 66 ]

= > 450 = ( n / 2 ) x 75

= > 450 x 2 / 75 = n

= > 12 = n

Therefore the number of terms is 12.

Now,

= > 12th term = last term = 66

= > a + ( 12 -1 )d = 66

= > 9 + 11d = 66

= > 11d = 55

= > d = 5

Therefore, the number of terms is 12 and the common difference between the terms is 5.