Math  Arithmetic & Geometric
posted by Student555 .
1) Given the terms a35 = 1238 and a70 = 1483 of an Arithmetic. Find the exact value of the term a105 a sequence and sum of sequence.
2) Given a3 = 99 and a5 = 891 of a Geometric. Find the exact value of the term a7 of the sequence and the sum of sequence.

1.
a+ 34d = 1238
a+69d = 1483
subtract them
35d = 245
d = 7
then in the 1st equation:
a + 238 = 1238
a = 1000
so term(105) = 1000 + 104(7) = 1728
2.
ar^2 = 99
ar^4 = 891
divide the 2nd by the third.
r^2 = 9
r = ±3
in the 1st
a(9) = 99
a = 11
then term(7)
= ar^6
= 11(3)^6 = 8019 
Thanks a lot

An arithmetic sequence is represented in the following table. Enter the missing term of the sequence.

Mathariyhmetic & geometric