Find the common difference d and the nth term of the arithme

Find the common difference d and the nth term of the arithmetic sequence whose 5th term is 11 and 13th term is 9. Now find the common difference d and the nth term if the 5th term is 13 and the 12th term is 48. Make sure to write all answers simplified and in integer form.

Solution

nthe term of arithmetic series is given by

a_n=a₀(n-1)d

d is the common difference and a₀ is the first term

According to question

a₅=a₀+4d=11

a₁₃=a₀+12d=9

Solving these equations we get

d=-1/4 and a₀=12

And in second question

a₅=a₀+4d=13

a₁₂=a₀+11d=48

Solving these equations we get

d=5 and a₀=-7