Find the common difference d and the nth term An of the arithmetic sequence 10th term is 33: 16th term is 35

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

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step-by-step explanation:

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step-by-step explanation:

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