Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. text({) 1/4, - 2/9, 3/16, - 4/25, ...text(})

The general term for the given sequence is:

Step-by-step explanation:

The given series is:

First of all, let us have a look at the positive and negative sign of the sequence.

2nd, 4th, 6th ..... terms have a negative sign.

For this we can use the following

i.e. Whenever 'n' is odd, power of (-1) will become even resulting in a positive term for odd terms i.e. (1st, 3rd, 5th ........ terms)

Whenever 'n' is even, power of (-1) will become odd resulting in a negative term for even terms i.e. (2nd, 4th, 6th ..... terms)

Now, let us have a look at the numerator part:

1, 2, 3, 4.....

It is simply .

Now, finally let us have a look at the denominator:

4, 9, 16, 25 ......

There are squares of the (n+1).

i.e. 1st term has a square of 2.

2nd term has a square of 3.

and so on

So, it can be represented as:

nth term of the sequence is:

seems like d

step-by-step explanation: