The eighth term of an arithmetic sequence is 25, and the 12th term is 41. What is the 51st term?

1 Answer
Mar 6, 2018

# 197#.

Explanation:

In the usual notation for an AP, we are given that,

#T_8=25, and, T_12=41#, and we seek for #T_51#.

Knowing that, #T_n=a+(n-1)d#, we have,

#T_8=25 rArr a+7d=25......(1)#, and, similarly,

# a+11d=41......(2)#.

Solving #(1) and (2), d=4, and, a=-3#.

Consequently,

#T_51=a+50d=-3+50xx4=-3+200=197#.