Answer:
1/3, 89/9
Step-by-step explanation:
Formula for an arithmetic projection is;
Tn = a + (n-1)d; where a is first term and d is the common difference.
Hence;
T10 = a + (10-1) d = 33.
Hence T10 = a + 9d = 33---------------(1)
T16 = a + (16-1) d = 35
T16 = a + 15 d = 35---------------(2)
Subtracting eqn(1) from (2)
a-a + 15d - 9d = 35-33
6d = 2
d = 2/6 = 1/3
From eqn (1)
a = 33-10d
a= 33- 10(1/3) = 33 -10/3 = 99-10/3 = 89/3
hence a = 89/3 , d = 1/3
But we are required to find the nth term which is defined as a×n according to the question.
Hence Tn =89/3 × 1/3 = 89/9 = 9 8/9
