Question

If the nth term of A.P. 12,15,18........99 is 99. Then value of n is equal to__________.

Answer 1

Answer: n = 30

Step-by-step explanation:

a=12 d=t2-t1= 15-12= 3. Tn = 99

Tn=a+(n-1)d

99=12+(n-1)3

87=3n-3

3n=90

n=30

Answer 2

The value of n is equal to 30.

Step-by-step explanation:

The given A.P.

12, 15, 18, ........, 99

Here, first term (a) = 12, common difference(d) = 15 - 12 = 3  and

$a_{n} =99$

To find, the value of n = ?

Let n be the number of terms.

We know that,

The nth term of an AP

$a_{n} =a+(n-1)d$

∴ 12 + (n - 1)3 = 99

⇒  (n - 1)3 = 99 - 12 = 87

⇒  n - 1 = $\dfrac{87}{3}$ = 29

⇒ n = 29 + 1 = 30

Thus, the value of n is equal to 30.