the common ratio of a g.p is 2.if the 5th term is greater than the first term by 45, find the 5tth term
If the first term of a GP is ‘a’ and the common ratio is r, then the n’th term is: ar^(n − 1).
5th term is greater than 1st term by 45. ar^4 - a = 45.
Substitute r = 2 in the expression.
a*2^4 - a = 45
16a - a = 45
15 a = 45
a = 3
5th term = ar^(5 -1) = 3 * 2^4 = 48
a × r^4 - a = 45
Where a= 2
a × 2^4 - a =45
a × 16 - a =45
16a - a= 45
15a =45
Divide through by 15
a = 3
Tn = ar^n-1
Where n= 5 ;a= 3 ; r= 2
T5 = 3 × 2^5 -1
T5 = 3 × 2^4
T5 = 48
U didn't really explain it well . I needed a full and understandable answer.
Very good
Well, well, well... looks like we're dealing with some geometric progression here! Let's have some fun with numbers, shall we?
So, we have a common ratio of 2, which means each term is twice the previous one. Now, if the 5th term is greater than the first term by 45, we can do a bit of math gymnastics.
Let's say the first term is "x". That means the 5th term would be 2^(5-1) * x, or 16x. And since the 5th term is greater than the first term by 45, we can set up an equation:
16x - x = 45
Simplifying that equation, we get:
15x = 45
Dividing both sides by 15, we find that x = 3.
So, the first term is 3. Now, to find the 5th term, we multiply the first term (3) by the common ratio (2) raised to the power of 5-1 (which is 4).
The 5th term = 3 * 2^4 = 3 * 16 = 48.
Voila! The 5th term is 48.
Hope that brought a smile to your face!
To find the 5th term of a geometric progression (G.P.), we can use the formula:
aₙ = a₁ * r^(n-1)
where:
aₙ represents the nth term of the G.P.
a₁ is the first term of the G.P.
r is the common ratio of the G.P.
n is the position of the term.
In this case, we are given that the common ratio (r) is 2. Let's assume that the first term (a₁) is 'x', and we need to find the 5th term (a₅).
We know that the 5th term (a₅) is greater than the first term (a₁) by 45. So, we can express this as:
a₅ = a₁ + 45
Substituting the values in the formula, we get:
a₅ = x * 2^(5-1)
a₅ = x * 2^4
Now, equating this with a₁ + 45, we have:
x * 2^4 = x + 45
To solve this equation for 'x', we simplify the equation by dividing both sides by 'x':
16 = 1 + (45/x)
Now, multiply both sides by 'x':
16x = x + 45
Subtract 'x' from both sides:
15x = 45
Divide both sides by 15:
x = 45 / 15
x = 3
Since we have found the value of x (the first term), we substitute it back into the formula to find the 5th term (a₅):
a₅ = 3 * 2^4
a₅ = 3 * 16
a₅ = 48
Therefore, the 5th term of the G.P. is 48.
Is g.p. supposed to mean geometric progression? You should not assume that we know that.
The fifth term will be 2^3 = 8 times the second term
a5 = 8 a2
a5 = a2 + 45
0 = 7 a2 -45
a2 = 45/7
a3 = 90/7
a4 = 180/7
a5 = 360/7
Check: a5 - a2 = 315/7 = 45