The given sequence is an arithmetic progression (A.P), which means that the difference between any two consecutive terms is a constant value. We are given the 7th and 9th terms of the sequence as 16 and 20 respectively, and we need to find the nth term of the sequence.

To solve this problem, we can use the formula for the nth term of an arithmetic progression, which is given by:

an = a + (n-1)d

where 'an' is the nth term of the sequence, 'a' is the first term, 'n' is the number of terms, and 'd' is the common difference between any two consecutive terms.

We can use the given information to form two equations, one for the 7th term and one for the 9th term:

a + 6d = 16 --(1)

a + 8d = 20 --(2)

Subtracting equation (1) from equation (2), we get:

2d = 4

Therefore, the common difference between any two consecutive terms is d = 2.

Now we can use equation (1) or (2) to find the value of the first term 'a':

a + 6(2) = 16

a = 4

Therefore, the first term of the sequence is a = 4.

Now we can use the formula for the nth term to find the value of the nth term:

an = a + (n-1)d

= 4 + (n-1)2

= 2n + 2

Therefore, the correct answer is option A: 2n+2.

To summarize, we used the given information about the 7th and 9th terms of an arithmetic progression to find the common difference and the first term of the sequence. Then we used the formula for the nth term of an arithmetic progression to find the value of the nth term.

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