arithmetic and geometric sequences

Question

Given the terms T10 = 3/512  and T15 = 3/16384  of a geometric sequences, find the exact value of the term T30 of the sequences

Answer 1

Geometrik sequens...term(n+1)=konst*term(n)

term10=3/512

term15=3/16384

term15/term10=(3/16384) / (3/512)

=512/16384=1/32  =(1/2)^5

so term(n+1)=(1/2)*term(n)

term30=(term15) / (2^15)

=(term15) / 32,768

=(3/16385) / 32768

=3/(536,903,680)

or 3 / 2^29

=3*2^-29

Answer 2

A geometric sequnce has all its terms positive. The first term is 7 and the thrid term is 28

What is the common ratio?

Find the sum of the first 14 terms

Answer 3

1,-6,36