Given the sequence 12, 7, 2, -3, ---.Find the value of n for which the nth term is -43.

The given sequence is an arithmetic sequence (or arithmetic progression) where each term after the first is obtained by subtracting a constant difference from the preceding term.

The common difference (d) in this sequence is 7 - 12 = -5.

The nth term (Tn) of an arithmetic sequence can be found using the formula:

Tn = a + (n - 1) * d

where:

• Tn is the nth term,
• a is the first term in the sequence,
• d is the common difference,
• n is the position of the term in the sequence.

We are asked to find the value of n for which the nth term is -43. We can set up the equation:

-43 = 12 + (n - 1) * -5

Solving for n gives:

-43 - 12 = (n - 1) * -5 -55 = (n - 1) * -5 55 = (n - 1) * 5 n - 1 = 55 / 5 n - 1 = 11 n = 11 + 1 n = 12

So, the 12th term of the sequence is -43.