Question

For each sequence write down the formula for the nth number and calculate the 11th number, the nth number, and the 100th number. 85, 67, 49, ...

Answer 1

nth number ; Tn = -18 n + 103

For the 11 th number : T₁₁ = -18 *11 +103 = -95

For the 100 th number : T₁₀₀ = -18 *100 + 103 = -1697

Explanation:

The sequence is given as;

85, 67, 49, ......

This is an A.P with a common difference ,d= -18

The formula for nth term can be written as;

Tn=d*n +???

where d= -18, then Tn= -18*n , Tn = -18 n +?

For;

n =1 ----- Tn = -18*1 = -18 ------but T₁ = 85 , so you add 103 to -18 to get 85

n=2-------Tn = -18*2 = -36------but T₂= 67 , so you add 103 to -36 to get 67

Thus,

For the nth number ;

Tn = -18 n + 103

and

For the 11 th number : T₁₁ = -18 *11 +103 = -95

For the 100 th number : T₁₀₀ = -18 *100 + 103 = -1697