Question

Find the n^(th ) term (T_(n)) for an arithmetic sequence with a=23,d=-4. Hence find m such that T_(m)=3.

Answer 1

The formula to find the nth term (Tn) of an arithmetic sequence is Tn = a + (n-1)d. By substituting the given values of a and d, we can find the nth term. To find m such that Tm = 3, we can set 3 equal to the formula for Tn and solve for m. The solution is m = 20.25.

Step-by-step explanation:

The formula to find the nth term (Tn) of an arithmetic sequence is:

Tn = a + (n-1)d

For this question, a = 23 and d = -4. Substituting these values into the formula, we get:

Tn = 23 + (n-1)(-4)

To find m such that Tm = 3, we can set 3 equal to the formula for Tn and solve for m:

3 = 23 + (m-1)(-4)

Simplifying the equation, we get:

4m - 81 = 0

Solving this quadratic equation, we find that m = 20.25.