For a given arithmetic sequence the 73rd term a73 is equal t

For a given arithmetic sequence, the 73^rd term, a_73, is equal to -382, and the 11^th term, a_11, is equal to -72. Find the value of the 34^th term, a_34. a_34 =

Solution

The n^th term of arithmetic series is given by

a_n=a₀+(n-1)d

a₇₃= a₀+72d

-382= a₀+72d

a₁₁=a₀+10d

-72=a₀+10d

Solving -382=a₀+72d and -72=a₀+10d for a₀ and d we get

a₀=-22 and d=-5

a₃₄= -22 +(34-1)(-5) = -22 - 165= -187

Hence the 34^th term is -187