Question

If for an AP a5=a10=5a , then a15 is a) 12a b)-12a c)13a d)-13a

Answer 1

Answer:

15a.

Step-by-step explanation:

From the properties of AP :

     nth term = a + ( n - 1 )d             { where a is the first term and d is the common difference is d}

Here, first term is a, let the common difference be d.

⇒ Given,

             a₅ = a₁₀ = 5a

⇒ a + ( 5 - 1 )d = a + ( 10 - 1 )d = 5a

⇒ a + 4d = a + 9d = 5a

⇒ a + 4d = 5a    and   a + 9d = 5a

⇒ 4d = 5a - a   and    9d = 5a - a

⇒ 4d = 4a          and   9d = 4a

⇒ d = a       and (9/4)d = a  

          Taking the first case : a = d

⇒ a₁₅ = a + ( 15 - 1)d

         = a + 14d

         = a + 14a

         = 15a

Answer 2

GiVeN : -

A AP is given in which a5 = a10 = 5a

To FiNd :-

• => a15 = ?

SoLuTiOn : -

We know that,

• an = a + (n-1)d

From the question it is given that,

=> a5 = 5a ---(1)

=> a10 = 5a ---(2)

So,

a5 = a + 4d = 5a. -( From - 1)

=> a + 4d = 5a

=> 4d = 4a

=> d = a. ---(3)

Now,

a15 = a + 14d.

a15 = a + 14 × a = 15a or = d + 14d = 15d