find sum of d followingG.p.
30+15+7 1÷2+3 3÷4………as far as the 8 term.pls using fomula 2
Reading that as:
30 + 15 + 7 1/2 + 3 3/4 + ....
so a = 30, r = 1/2
sum(8) = 30(1 - (1/2)^8)/(1 - 1/2)
= 30( 1 - 1/256)/(1/2)
= 60(255/256) = 3825/64
check my arithmetic
G p
To find the sum of the given geometric progression (G.P.) using the formula, we need to identify the first term (a), the common ratio (r), and the number of terms (n).
In this case, the first term, a = 30, and the common ratio, r = 1/2.
To find the number of terms (n), we can use the formula for the nth term of a G.P., which is given by:
nth term (Tn) = a * r^(n-1)
Given that the 8th term is not provided, we can use the formula to find the value of the 8th term:
T8 = 30 * (1/2)^(8-1)
T8 = 30 * (1/2)^7
T8 = 30 * (1/2)^6 * (1/2)
T8 = 30 * (1/64) * (1/2)
T8 = 30/128
T8 = 15/64
Now that we have the first term (a), the common ratio (r), and the number of terms (n = 8), we can use the formula to find the sum (S) of the G.P.:
S = a * (1 - r^n) / (1 - r)
S = 30 * (1 - (1/2)^8) / (1 - 1/2)
S = 30 * (1 - (1/64)) / (1/2)
S = 30 * (63/64) / (1/2)
S = 30 * (63/64) * (2/1)
S = 30 * 63 * 2 / 64
S = 1890/64
S ≈ 29.53125
Therefore, the sum of the given G.P. up to the 8th term (using the formula) is approximately 29.53125.
To find the sum of a geometric progression (G.P.) using a formula, we need to use the formula for the sum of a G.P., which is:
Sum = (first term * (1 - common ratio ^ number of terms)) / (1 - common ratio)
In this case, the first term (a) is 30, and the common ratio (r) is 1/2.
Now, let's find the common ratio for the given G.P.:
30, 15, 7 1/2, 3 3/4, ...
To find the common ratio, we divide each successive term by the preceding term:
15/30 = 1/2
(7 1/2) / 15 = 1/2
(3 3/4) / (7 1/2) = 1/2
Since all the ratios are equal to 1/2, the common ratio is 1/2.
Now, we can find the sum of the G.P. up to the 8th term using the formula:
Sum = (30 * (1 - (1/2)^8)) / (1 - 1/2)
Calculating this expression:
Sum = (30 * (1 - (1/256))) / (1/2)
= (30 * (255/256)) / (1/2)
= 30 * (255/256) * (2/1)
= 30 * 255 * 2 / 256
= 15 * 255
= 3825
Therefore, the sum of the given geometric progression up to the 8th term is 3825.