Write an equation for the nth term of the arithmetic sequence -4, 1, 6, 11,... . Then find a50. An equation is an=_n-_ && a50=

Question

kinda stuck need help on this problem

Answer 1

The explicit form of an arithmetic sequence is:

a_n = a₁ + (n-1)d

Where:

1. n is the term number (n = 1, 2, 3, ...)
2. a_n is the nth term in the sequence
3. a₁ is the first term in the sequence = -4
4. d is the common difference

To find the common difference, subtract any two successive terms: 1 - (-4) = 5, 6 - 1 = 5, 11 - 6 = 5. So we have d = 5. Hence the explicit form for this sequence is:

a_n = -4 + (n-1)5

To find a₅₀, set n = 50 in the above formula and compute the answer.