Question

find the nth term of the sequence 5 8 11 14

Answer 1

The nth term is 3n+2.

The given sequence is in A.P.
Here,
First term,a= 5
Common difference,d= 3
Therefore the nth term = a+(n-1)d =5+(n-1)3
=5+3n-3 =3n+2.

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Answer 2

The nth term of the sequence 5 8 11 14  is 3n + 2

Given:

• sequence 5 8 11 14

To Find:

• nth Term of the sequence

Solution:

Arithmetic sequence  

• Sequence of terms in which difference between one term and the next is a constant.
• This is also called Arithmetic Progression AP
• Arithmetic sequence can be represented in the form :
• a, a + d  , a + 2d , …………………………, a + (n-1)d
• a = First term
• d = common difference = aₙ-aₙ₋₁
• nth term =  aₙ =  a + (n-1)d  
• Sₙ = (n/2)(2a + (n - 1)d)
• Sum of Arithmetic sequence (AP) is called Arithmetic series

Step 1:

Find Difference between consecutive term

8 - 5 = 3

11 - 8 = 3

14 - 11 = 3

As Difference is constant hence sequence is Arithmetic sequence

Step 2

Find nth term by substituting a = 5 , d = 3

nth term =  aₙ =  a + (n-1)d

=> nth term =  aₙ =  5+ (n-1)3

=> nth term =  aₙ =  5 + 3n - 3

=> nth term =  aₙ =  3n + 2

The nth term of the sequence 5 8 11 14  is 3n + 2

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