For each arithmetic sequence, determine

a) the value of t1 and d (2 marks)
b) an explicit formula for the general term (2 marks)
c) t20 (2 marks)

7/4, 1, 1/4, -1/2

t1 = 7/4

d = -3/4

Tn = 7/4 - 3/4 (n-1)

...

To determine the value of t1 and d for the given arithmetic sequence, follow these steps:

Step 1: Identify the first term, t1.
The first term of the sequence is the initial value given in the sequence, which is 7/4.

Step 2: Identify the common difference, d.
The common difference is the constant value added (or subtracted) at each step to obtain the next term in the sequence.

To find the common difference between any two consecutive terms in the sequence, subtract the first term from the second term:

1 - 7/4 = 4/4 - 7/4 = -3/4

Therefore, the common difference (d) is -3/4.

a) The value of t1 is 7/4, and d is -3/4.

To find the explicit formula for the general term, use the formula:

tn = t1 + (n-1)d

where tn represents the nth term, t1 is the first term, n represents the position of the term, and d is the common difference.

b) Explicit formula:
tn = 7/4 + (n-1)(-3/4)

c) To find t20 (the 20th term in the sequence), substitute n = 20 into the formula:

t20 = 7/4 + (20-1)(-3/4)
= 7/4 + 19(-3/4)
= 7/4 - 57/4
= -50/4
= -25/2

Therefore, t20 is -25/2.