Question

1/2,3/2,5/2,7/2,9/2.....then find nth term​

Answer 1

Answer: 1/2,3/2,5/2,7/2,9/2....

=1/2,1/2+1,1/2+2,1/2+3........

=tn=a+(n-1)d

=1/2+(n-1)1

=n-1/2

a= first term

d=common difference

Tn=nth term

Answer 2

The nth term of the given AP($a_{n}$) is equal to (n - $\dfrac{1}{2}$).

Step-by-step explanation:

The given series:

$\dfrac{1}{2} ,\dfrac{3}{2}, \dfrac{5}{2}, \dfrac{7}{2},\dfrac{9}{2},........$

Here, first term (a) = $\dfrac{1}{2}$, common difference(d) = $\dfrac{3}{2} -\dfrac{1}{2}=\dfrac{2}{2} =1$ and

the number of terms = n

The given series are in AP.

To find, the nth term of the given AP($a_{n}$) = ?

We know that,

The nth term of the AP

$a_{n} =a+(n-1)d$

= $\dfrac{1}{2}$ + (n - 1) × 1

= $\dfrac{1}{2}$ + n - 1

= n + $\dfrac{1}{2}$ - 1

= n - $\dfrac{1}{2}$

∴ The nth term of the given AP($a_{n}$) = (n - $\dfrac{1}{2}$)

Thus, the nth term of the given AP($a_{n}$) is equal to (n - $\dfrac{1}{2}$).