Question

the sum of the first two terms of a GP is 28,but the sum of the third and fourth terms is 252.find the second term of the gp if the seventh term is 5103. please help.

Answer 1

a + ar = 28

ar^2 + ar^3 = 252

a(1+r) = 28
ar^2(1+r) = 252

ar^2(1+r)/a(1+r) = r^2 = 252/28 = 9
r = 3 or -3

a(1-3) = 28 ==> a = -14
a(1+3) = 28 ==> a = 7

So, now we need to know that

ar^6 = 5103
7*3^6 = 5103
Unfortunately, that works whether r is 3 or -3

Using r = -3

7+(-21) = -14
7+21 = 28

So, r=3

7r = 21

The bit about the 7th term is redundant and unhelpful.

Answer 2

Thanks for the solution

Answer 3

Thanks 4 d answer

Answer 4

Thanks for the reasonable solution

Answer 5

Nice one

Answer 6

How can I get the second term of the gp if the seventh term is 5103

Answer 7

Thanks for the help

Answer 8

thank for the help

Answer 9

[AI-generated answer — Explain Bot]

To solve this problem, we need to first find the common ratio (r) of the geometric progression (GP).

Let's assume the first term of the GP is 'a' and the common ratio is 'r'.

The sum of the first two terms can be written as:
S1 = a + ar

Given that S1 = 28, we have:
28 = a + ar

Next, the sum of the third and fourth terms can be written as:
S2 = ar^2 + ar^3

Given that S2 = 252, we have:
252 = ar^2 + ar^3

Now, we need to find the common ratio 'r' and use it to find the second term.

To find 'r', we can divide the second equation (S2) by the first equation (S1). This will eliminate 'a' from the equation.

252/28 = (ar^2 + ar^3)/(a + ar)

Simplifying this expression, we get:
9 = r^2 + r^3

Now, we have obtained a cubic equation in terms of 'r'. By solving this equation, we can find the possible values of 'r'. Then we can substitute the value of 'r' into the first equation to find 'a', and finally use 'a' and 'r' to find the second term.

However, solving a cubic equation can be complex and time-consuming. Therefore, I recommend using a numerical method or a calculator to find the value of 'r'. To do this, you can use the trial and error method or utilize mathematical software or online calculators specifically designed to solve equations.

Once you have obtained the value of 'r', you can substitute it into the first equation (28 = a + ar) to solve for 'a'. Finally, use 'a' and 'r' to find the second term of the GP, which is the term after the first term.