Find the first term (a) of ago sequince in which the common ratio is 2 and sum of the first 10 terms are 93
I will assume this is an arithmetic sequence.
Let's just use our formulas
we know d = 2
sum(10) = 93 ---> n = 10, a = ?
(10/2)(2a + 9(2)) = 93
5(2a + 18) = 93
10a + 90 = 93
10a = 3
a = .3
check:
10th term = a+9d = .3 + 18 = 18.3
sum(10) = (10/2)(first + last) = 5(.3+18.3) = 93
a common ratio indicates a g.p. (or, as nasra calls it, a go)
S10 = a(r^10-1)/(r-1)
a(2^10-1) = 93
a = 93/1023
and that's "the sum ... is 93"
To find the first term (a) of an arithmetic sequence, where the common ratio (r) is 2 and the sum of the first 10 terms is 93, you can use the formula for the sum of an arithmetic sequence:
S = (n/2) * (2a + (n-1)d),
where S is the sum of the terms, n is the number of terms, a is the first term, and d is the common difference.
In this case, we are given that the common ratio (r) is 2, which means the common difference (d) is obtained by subtracting the previous term from the next term. In an arithmetic sequence, the common ratio (r) and common difference (d) are the same.
Since the common ratio is 2, the common difference (d) is also 2.
Now, let's use the given information to find the first term (a). We are given that the sum of the first 10 terms (S) is 93.
S = (10/2) * (2a + (10-1)*2),
93 = 5 * (2a + 18),
93 = 10a + 90,
10a = 3,
a = 3/10 = 0.3.
Therefore, the first term (a) of the arithmetic sequence is 0.3.