The nth term of a sequence is given by T= an−b , when a and b are constant If the 5th and 13th term are 10 and 34 respectively . Find the 25th term

The nth term of the sequence is given by T = an - b.
We are given:
The 5th term (T₅) is 10.
The 13th term (T₁₃) is 34.

Substitute these values into the formula:
For T₅ = 10:
10 = a(5) - b
5a - b = 10 (Equation 1)

For T₁₃ = 34:
34 = a(13) - b
13a - b = 34 (Equation 2)

Subtract Equation 1 from Equation 2 to eliminate 'b':
(13a - b) - (5a - b) = 34 - 10
13a - b - 5a + b = 24
8a = 24
a = 24 / 8
a = 3

Now substitute the value of 'a' (a=3) into Equation 1:
5(3) - b = 10
15 - b = 10
-b = 10 - 15
-b = -5
b = 5

Substitute the values of a=3 and b=5 into the general formula T = an - b:
T = 3n - 5

Substitute n = 25 into the formula T = 3n - 5:
T₂₅ = 3(25) - 5
T₂₅ = 75 - 5
T₂₅ = 70

The 25th term is 70.