I have to find the five terms in geometric sequence in this
a(lower n)= (2)^n-1
I would do it 2(1)+2(2)+(2(3)+2(4)+2(5)
so 2,4,6,8,10
Did I do this correctly??
Nope. 2^n goes
2,4,8,16,32,64,...
So, 2^n-1 goes
1,3,7,15,31,63,...
Your sequence is 2*n, not 2^n
Actually, none of the sequences I gave is a geometric sequence. For that you need
an = 2^(n-1)
1,2,4,8,16,...
where each pair of terms has a common ratio, in this case, 2.
To find the five terms in a geometric sequence using the given formula, you should substitute the values of n from 1 to 5 into the formula and calculate the corresponding terms. Let's go step by step.
Formula given: a(n) = 2^(n-1)
Substituting n = 1 into the formula:
a(1) = 2^(1-1) = 2^0 = 1
Substituting n = 2 into the formula:
a(2) = 2^(2-1) = 2^1 = 2
Substituting n = 3 into the formula:
a(3) = 2^(3-1) = 2^2 = 4
Substituting n = 4 into the formula:
a(4) = 2^(4-1) = 2^3 = 8
Substituting n = 5 into the formula:
a(5) = 2^(5-1) = 2^4 = 16
So, the correct terms in the geometric sequence are 1, 2, 4, 8, and 16. Therefore, you did not find them correctly.