The 3rd and 9th term of a g.p are 54 and 39,336 respectively.find the 6th term,sum of 4th term,sum of 4th and 7th term and product of 2nd and 5th term
"3rd and 9th term of a g.p are 54 and 39,336"
--> ar^2 = 54 and ar^8 = 39336
ar^8/(ar^2) = 39336/54
r^6 = 728.444.. , I suspect that was supposed to be 729 , since 3^6 = 729
I will go with r = ± 3
then in ar^2 = 54
9a = 54 , ----> a = 6
so your typo was in 9th term is 39366 instead of your 39336
take the rest from there
The 3rd and 9th term of a GP are 54 and 39366. Respectively find the following (a) 6th term (b)sum of the 4th and 7th terms (c) product of the 2nd and 5th terms.
there are 6 terms between 54 and 39336, so
r^6 = 39336/54 = 6556/9
I suspect a typo, since it is not rational.
Anyway, use that or fix it, and you will have r.
Then a = 54/r^2
Having a and r, you can find any other terms.
"sum of 4th term" makes no sense.
the 3rd and 9th term of a gp are 54 and 39366 respectively. find the 6th term
I need the answer
The third and the nineth terms of a GP are 54and 39366 respectively. Find the sixth terms and the sum of the 4th term and the sum of infinity
To find the 6th term of the geometric progression (g.p.), we need to determine the common ratio (r) first.
Using the formula for nth term of a g.p., we can write the equation for the 3rd term as:
a × r² = 54 ...(1)
Similarly, for the 9th term, we have:
a × r⁸ = 39336 ...(2)
Dividing equation (2) by equation (1), we get:
r⁸/r² = 39336/54
r⁶ = 729
r = 3
Now we know the common ratio (r = 3).
To find the 6th term, we can use the formula for nth term of a g.p.:
a × r⁵ = a × 3⁵ = a × 243
We can find the value of 'a' by substituting the value of the 3rd term (54):
54 × r² = a × 3²
54 × 9 = a × 9
a = 6
Thus, the 6th term of the g.p. is:
6 × 243 = 1458
To find the sum of the 4th term, we can again use the formula for nth term of a g.p.:
a × r³ = a × 3³ = a × 27
Summing the 4th term involves adding the terms from the 1st term to the 4th term.
The sum of n terms in a g.p. can be calculated using the formula:
Sum(n) = a × (rⁿ - 1) / (r - 1)
Substituting n = 4, a = 6, and r = 3, we can find the sum of the first 4 terms:
Sum(4) = 6 × (3⁴ - 1) / (3 - 1)
= 6 × (81 - 1) / 2
= 6 × 80 / 2
= 6 × 40
= 240
The sum of the 4th and 7th terms can be found by summing the terms from 1st to 4th and from 1st to 7th.
Again using the formula for the sum of n terms, we find:
Sum(7) = a × (r⁷ - 1) / (r - 1)
Substituting n = 7, a = 6, and r = 3, we can calculate the sum of the first 7 terms:
Sum(7) = 6 × (3⁷ - 1) / (3 - 1)
= 6 × (2187 - 1) / 2
= 6 × 2186 / 2
= 6 × 1093
= 6558
The product of the 2nd and 5th terms can be calculated as:
a × r × r⁴ = a × r⁵
Substituting a = 6 and r = 3, we get:
6 × 3⁵ = 6 × 243
= 1458
Therefore, the 6th term is 1458, the sum of the 4th term is 240, the sum of the 4th and 7th terms is 6558, and the product of the 2nd and 5th terms is 1458.