Thread: algebra problems

please friends help me outwith these sums

1)If the sum of first n terms of two arithmetic progression are in the ratio
(7n + 1) 4n + 27), find the ratio of their 11th terms.

2)Find the sum of first n terms of the series
3 × 8 + 6 ×11 + 9 × 14 + ....

3)Let f(x) = x2 + 3, g(x) = x – 2, then find fog and gof. Also, show that (fog) (3/2) =(gof) (3/2).

4)Solve the equation:
Sin x + Sin 2x + Sin 3x + Sin 4x = 0

Originally Posted by rizwanrivz

please friends help me outwith these sums

1)If the sum of first n terms of two arithmetic progression are in the ratio
(7n + 1) 4n + 27), find the ratio of their 11th terms.

sol1]
let the first series be a ,a+d,a+2d,.....

the second series be A,A+D, A+2D,.......
given s/S=(7n+1)4n+27)

TO FIND--------- t11/T11=? .............t11 denotes 11th term of first AP
and T11 denotes 11th term of Second AP

s=n/2*[2a+(n-1)d] ................................. sum of first AP upto n terms

similarly sum of second AP is

S=n/2*[2A+(n-1)D]

s/S=(7n+1)4n+27)

[n/2*{2a+(n-1)d}] / [n/2*{2A+(n-)D}]=(7n+1)4n+27)

n/2 gets cancelled we get

[2a+(n-1)d]/ [2A+(n-)D]=(7n+1)4n+27)

dividing nr.& dr. of LHS by2 we get

[a+(n-1)d/2] / [A+(n-1)D/2] = (7n+1)4n+27)

now put n=21 both sides we get

[a+10d]/[A+10D]=148/111

t11/T11=148/111

Originally Posted by rizwanrivz

please friends help me outwith these sums

1)If the sum of first n terms of two arithmetic progression are in the ratio
(7n + 1) 4n + 27), find the ratio of their 11th terms.

Sum of n terms of an A.P.

Put and for two APs and d1 and d2 respectively as the common difference
so

Here take out 2 as common and cancel it ie;


Now here put the value of this will give you the value of n

Originally Posted by rizwanrivz

please friends help me outwith these sums


2)Find the sum of first n terms of the series
3 × 8 + 6 ×11 + 9 × 14 + ....

the general term of the given series is Tn=3n*(3n+5)

Tn=9n^2+15n

now taking summation both sides
ΣTn=9*Σn^2 + 15*Σn................................(1)

now we know that
Σn=n(n+1)/2
and Σn^2=n(n+1)(2n+1)/6
put this in eq. (1) and get the answer

Originally Posted by rizwanrivz

please friends help me outwith these sums



3)Let f(x) = x2 + 3, g(x) = x – 2, then find fog and gof. Also, show that (fog) (3/2) =(gof) (3/2).

fog(x)= (x-2)^2+3
and
gof(x)=x^2+3-2

Put 3/2 in both of them and check yourself

Hello, rizwanrivz!

For #4, we need two sum-to-product identities:

. .

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4) Solve the equation: .

. . . .

Factor:. .

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. . . . . . . . .


Then: .