# Geomatic Sequence

posted by Nina

In a geomatic sequence, the seventh term exceeds the fifth term by 1920. Find the sum of the first eleven terms if the common ratio of the sequence is 2.

1. Steve

that's geometric sequence

T7 = T5*r^2 = T5+1920
r = 2, so

4*T5 = T5 + 1920
3T5 = 1920
T5 = 640

640 = 2^4 * 40

So, a=40 and the sequence is

40 80 160 320 640 1280 2560 5120 10240 20480 40960 ...

Note that 2560 = 640 + 1920

2. Reiny

ar^6 - ar^4=1920
64a-16a=1920
48a=1920
a = 40

sum(11) = 40(2^11 - 1)/(2-1) = 81880

3. Steve

oops - good catch, Reiny. You actually answered the question :-)

4. stephanie

find the fifth term in the sequence a1=-4a2=8a3=-16 can you guys help me

## Similar Questions

1. ### Math

A sequence is formed by adding together the corresponding terms of a geometric sequence and and an arithmetic sequence.The common ratio of the geometric sequence is 2 and the common difference of the arithmetic sequence is 2.The first …
2. ### math30

Sequences 1)A sequence has a first term of 24 and every other term is one half of the previous term. a)Write the first four terms of the sequence. b)Find a recursive formula that defines this sequence. c)Find an explicit formula that …
3. ### Arithmetic Sequence

Given the third term of an arithmetic sequence less than the fourth term by three. The seventh term is two times the fifth term. Find the common difference and the first term.
4. ### Geomatic Sequence

In a geomatic sequence, the 7th term exceeds the 5th term by 48. Find the first term if the common ratio is 2.
5. ### Maths

1..The first 2 terms of a geometric progression are the same as the first two terms of an arithmetic progression.The first term is 12 and is greater than the second term.The sum of the first 3 terms od the arithmetic progression is …
6. ### math

in an arithmetic sequence the common difference is equal to 2.the first term is also the first term of a geometric sequence. the sum of the first 3 terms of an arithmetic sequence and the sum of the first 9 terms of an arithmetic sequence …
7. ### maths

given 1,0.5,4,o.25,7,0.125,10 assume this pattern continues consistently 1.write down the 33th term in this sequence 2.determine the sum of the first 24 terms in this sequence.give the answer to five decimal place 2.1.in a geometric …
8. ### Math

1. The fourth and seventh terms of a geometric sequence are 6 and 384, respectively. What is the common ratio and the sixth term of the sequence?
9. ### math

The 1st,5th,13th term of an arithmetic sequence are the first 3 terms of geometric sequence with a common ratio of 2. If the 21st term of the arithmetic sequence is 72, calculate the sum of the first 10 terms of the geometric sequence.
10. ### Algebra

I am so lost on these problems. Write a geometric sequence that starts with 3 and has a common ratio of 5. What is the 23rd term in the sequence. Write an arithmetic sequence that has a common difference of 4 and the eighth term is …

More Similar Questions