Question

if an = 6n + 1 , find AP , a10 and d​

Answer 1

Required Answer:-

Given a relation for finding the AP:

• an = 6n + 1 where n denotes the number of times. Like if we want to find 1st term, then n = 1$.$

Now,

Putting n = 1,

➙ a1 = 6(1) + 1

➙ a1 = 7

Putting n = 2

➙ a2 = 6(2) + 1

➙ a2 = 13

Then, d = a2 - a1 because their is a common difference between any two terms of an AP. Hence,

➙ d = a2 - a1

➙ d = 13 - 7

➙ d = 6

Now, finding the AP: 7, 13, 19, 25....Keep on adding 6 to the previous term to get the next term.

To find a10, we need put n = 10,

➙ a10 = 6(10) + 1

➙ a10 = 60 + 1

➙ a10 = 61

Answer 2

Hope it helps you!

Step-by-step explanation:

Given:

• nth term = 6n+1

To find:

• AP
• 10th term
• d

Solution:

According to the given, we are going to consider the n as 1,2,3,4 in order to obtain the AP

If n=1,

• a = 6×1+1
• a = 6+1
• a = 7

If n = 2,

• a2(Second term) = 6×2+1
• Second term = 12+1
• Second term = 13

If n = 3,

• a3(Third term) = 6×3+1
• Third term = 18+1
• Third term = 19

Clearly, we obtained that our AP is: 7,13,19...

We know that, Common difference(d) = a2 - a1

=> d = 13-7

=> d = 6

Now, let us find the 10th term of the AP:

• an = a+(n-1)d

=> a(10) = 7+(10-1)×6

=> 10th term = 7+9×6

=> 10th term = 7+54

=> 10th term = 61