Question
27. Find the sum of 7 terms of the G.P 12, 6,
3……
A. 23.76
B. 27.36
C. 26.73
D. 23.81
3……
A. 23.76
B. 27.36
C. 26.73
D. 23.81
Answers
Answered by
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To find the sum of the first 7 terms of a geometric progression (G.P), we can use the formula:
S_n = a(r^n - 1)/(r - 1)
Where:
- S_n is the sum of the first n terms
- a is the first term of the G.P
- r is the common ratio
- n is the number of terms
In this case, the first term (a) is 12 and the common ratio (r) is 1/2 (since each term is divided by 2 to get the next term). The number of terms (n) is 7.
Plugging these values into the formula, we get:
S_7 = 12(1/2^7 - 1)/(1/2 - 1)
= 12(1/128 - 1)/(-1/2)
= 12(1/128 - 1)/(-1/2)
= 12(-127/128)/(-1/2)
= 12 * (-127/128) * (-2/1)
= 24 * 127/128
= 3048/128
= 23.81
Therefore, the sum of the first 7 terms of the G.P 12, 6, 3... is approximately 23.81.
The correct option is D. 23.81.
S_n = a(r^n - 1)/(r - 1)
Where:
- S_n is the sum of the first n terms
- a is the first term of the G.P
- r is the common ratio
- n is the number of terms
In this case, the first term (a) is 12 and the common ratio (r) is 1/2 (since each term is divided by 2 to get the next term). The number of terms (n) is 7.
Plugging these values into the formula, we get:
S_7 = 12(1/2^7 - 1)/(1/2 - 1)
= 12(1/128 - 1)/(-1/2)
= 12(1/128 - 1)/(-1/2)
= 12(-127/128)/(-1/2)
= 12 * (-127/128) * (-2/1)
= 24 * 127/128
= 3048/128
= 23.81
Therefore, the sum of the first 7 terms of the G.P 12, 6, 3... is approximately 23.81.
The correct option is D. 23.81.