THE 8TH TERM OF A GP=-7/32 FIND IT'S COMMON RATIO,IF IT'S 1ST TERM IS 28
To find the common ratio of a geometric progression (GP) and its 8th term, we can use the formula for the nth term of a GP:
an = a1 * r^(n-1)
Given:
a8 = -7/32
a1 = 28
We can substitute these values into the formula:
-7/32 = 28 * r^(8-1)
Simplifying the equation:
-7/32 = 28 * r^7
Now, we can isolate the common ratio (r) by dividing both sides of the equation by 28:
(-7/32) / 28 = r^7
Simplifying further:
-1/128 = r^7
To find the value of r, we can take the seventh root of both sides of the equation:
r = ( -1/128 )^(1/7)
Calculating this value, we get:
r ≈ -0.5
Therefore, the common ratio (r) of the geometric progression is approximately -0.5.
To find the common ratio of a geometric progression (GP), we can use the formula:
\[ \text{{Term}}_n = \text{{Term}}_1 \cdot \text{{Common Ratio}}^{(n-1)} \]
In this case, we are given the 8th term of the GP as \(-\frac{7}{32}\) and the 1st term as 28.
So we can write:
\[-\frac{7}{32} = 28 \cdot \text{{Common Ratio}}^{(8-1)}\]
Simplifying the above equation, we have:
\[-\frac{7}{32} = 28 \cdot \text{{Common Ratio}}^7\]
Now, divide both sides of the equation by 28 to get:
\[\frac{-7}{32 \cdot 28} = \text{{Common Ratio}}^7\]
Simplifying further:
\[\frac{-1}{128} = \text{{Common Ratio}}^7\]
To find the 7th root of both sides, we get:
\[\text{{Common Ratio}} = \left(\frac{-1}{128}\right)^{\frac{1}{7}}\]
Using a calculator to evaluate the above expression, we find that the common ratio is approximately -0.5
8th term of GP is -7/32 ----> ar^7 = -7/32
but a = 28
28r^7 = -7/32
r^7 = -7/896 = -1/128
take it from here ,
hint: what number raised to the 7th is 128, it will be the first simple number you'll try.