Question

if the nth term of the ap -1,4,9,14....is129 find the value of n.​

Answer 1

Given :-

• An AP, -1, 4, 9, 14, ...
• nth term = 129

To Find :-

• Value of n.

Solution :-

AP = -1, 4, 9, 14, ...

Let's find the common difference of the given AP which is the difference between each consecutive term and is denoted by d.

⇒ d = Second term - First term

⇒ d = 4 - (-1)

⇒ d = 4 + 1

⇒ d = 5

Now, from the given AP, it is clear that the first term of the AP which is denoted by a is -1.

So, we have:

• Common difference, d = 5
• First term, a = -1
• nth term, aₙ = 129

Given that the nth term of the AP is 129.

Nth term is given by,

⇒ aₙ = a + (n - 1)d

Substitute the required values,

⇒ 129 = -1 + (n - 1)5

⇒ 129 + 1 = 5n - 5

⇒ 130 + 5 = 5n

⇒ n = 135/5

⇒ n = 27

Hence, the value of n is 27, which means the 27th term of the given AP is 129.

Answer 2

Answer:

n = 27

Step-by-step explanation:

Given -

A. P. = -1, 4, 9, 14...129

To find -

The nth term of 129

Solution -

Common Difference (d) = Second term - first term

= 4-(-1) = 4+1 = 5

d = 5

a = -1

a↓n = 129

nth term = a+(n-1)d

=> 129 = (-1)+(n-1)5

=> 129+1 = 5(n)-5(1)

=> 130 = 5n-5

=> 130+5 = 5n

=> 135 = 5n

=> 135÷5 = n

=> 27 = n

=> n = 27

Hence 129 is 27th term of given A. P.

hope it helps.