Question

B1=0,02 bn=312,5 n=7 найти q=? и Sn=?

Answer 1

Bn=b1*q^(n-1)
q^(n-1)=bn/b1
q^(n-1)=312,5/0,02=15625
q^(n-1)=5^6
n-1=6
n=7
S7=b1*(q^7-1)/(q-1)
S7=0,02(78125-1)/(7-1)=0,02*78124/6=1562,48/6=260 31/75

Answer 2

To find the value of 'q' and 'Sn' in the given arithmetic sequence, we'll use the formulas for the nth term (Bn) and the sum of the first 'n' terms (Sn) of an arithmetic sequence.

The nth term of an arithmetic sequence is given by the formula: Bn = B1 + (n - 1) * q

The sum of the first 'n' terms of an arithmetic sequence is given by the formula: Sn = (n / 2) * (B1 + Bn)

Given values: B1 = 0.02 Bn = 312.5 n = 7

We need to find 'q' and 'Sn'.

Step 1: Finding 'q': We have the formula for Bn: Bn = B1 + (n - 1) * q

Plugging in the known values: 312.5 = 0.02 + (7 - 1) * q 312.5 = 0.02 + 6q

Now, solve for 'q': 6q = 312.5 - 0.02 6q = 312.48 q = 312.48 / 6 q = 52.08

Step 2: Finding 'Sn': We have the formula for Sn: Sn = (n / 2) * (B1 + Bn)

Plugging in the known values: Sn = (7 / 2) * (0.02 + 312.5) Sn = 3.5 * 312.52 Sn = 1093.82

Therefore, the value of 'q' is 52.08, and the sum of the first 7 terms 'Sn' is 1093.82.