Question

find the sum of n term of A.P, whose k'th term is 5k+1

Answer 1

Answer:

Step-by-step explanation:

As, it is given that   k   th   term of the A.P.  is 5k   + 1.

therefore,

 ak   =   a   + (k   – 1)d

⇒   a   + (k   – 1)d   = 5k   + 1

⇒ a   +   kd   –   d   = 5k   + 1

now, on comparing the coefficient of   k, we get,

d = 5

and  

a   –   d   = 1

⇒   a   – 5 = 1

⇒   a   = 6

Answer 2

Given: kth term of an AP is 5k + 1

To find: The sum of it's first n terms

Solution:

We are given the general term of an AP which is 5k + 1, i.e.

• ak = 5k + 1

Put k = 1 to get first term

⇒ a1 = 5(1) + 1

⇒ a1 = 5 + 1

⇒ a1 = 6

Put k = 2 to get second term

⇒ a2 = 5(2) + 1

⇒ a2 = 10 + 1

⇒ a2 = 11

So, in the AP we have:

• First term, a = a1 = 6

• Common difference, d = a2 - a1 = 11- 6 = 5

We have formula to find sum of n terms:

⇒ Sn = n/2[2a + (n - 1)d]

⇒ Sn = n/2[2(6) + (n - 1)(5)]

⇒ Sn = n/2[12 + 5n - 5]

⇒ Sn = n/2[7 + 5n]

This is the required sum of first n terms.