the first three terms of an ap are x, (3x +1) and (7x -4). Find the value x and 10th term

In A.P.

a1 = initial term of arithmetic progression

d = common difference

nth term of A.P.

an = a1 + ( n - 1 ) d

In this case a1 = x , a2 = 3 x + 1 , a3 = 7 x - 4 so:

a1 = x

a2 = a1 + ( 2 - 1 ) d

a2 = a1 + d

3 x + 1 = x + d

a3 = a1 + ( 3 - 1 ) d

a3 = a1 + 2 d

7 x - 4 = x + 2 d

Now you must solve system:

3 x + 1 = x + d

7 x - 4 = x + 2 d

Ttry it.

The solutions are:

x = 3 , d = 7

a1 = x = 3

an = a1 + ( n - 1 ) d

a10 = a1 + ( 10 - 1 ) d

a10 = a1 + 9 d

a10 = 3 + 9 ∙ 7 = 3 + 63 = 66

Your A.P.

3 , 10 , 17 , 24 , 31 , 38 , 45 , 52 , 59 , 66 ...

Proof:

a1 = x = 3

a2 = 3 x + 1

10 = 3 ∙ 3 + 1 = 9 + 1 = 10

a3 = 7 x - 4

17 = 7 ∙ 3 - 4 = 21 - 4 = 17

please solve it clear

[(7 x - 4 = x + 2 d) - (3 x + 1 = x + d)] => 4 x - 5 = d

substitute the value of d(4 x - 5) into any of the equations (7 x - 4 = x + 2 d) or (3 x + 1 = x + d)

Nice work

wow that's so brilliant

I dont understand how did got 63

X,(3x+1), and (7x-4)

Soln
Arithmetic mean: b=a+c ÷2
b=3x+1, a= x, c=7x-4
3x+1= x + 7x-4/2
Cross multiply
2(3x+1) = ×+7x-4
6x+2 = 8x-4
Collect like terms
6x-8x = -4-2
-2x =-2
Divide through with -2
Therefore x= 1

The others are using the wrong formula to truly find the first three terms of an Ap the arithmetic mean's formula does the job

Nice one I love it🤞

i am not sure I understand the answer

I don't understand

I don't understand

What about the first seven terms of progression?

U

Let T1=x

T2=3x+1
T3=7x-4
-T1=x
-T2=a1+(2-1)d
T2=a1+d
Substitute T2 in the eqn above
3x+1=x+d......(I)
-T3=a1+(3-1)d
T2=a1+2d
Substitute T3 in the eqn above
7x-4=x+2d.....(ii)
Equate both eqn to zero
- 3x+1-x-d=0
=2x+1-d=0.....(iii)
- 7x-4-x-2d=0
=6x-4-2d=0....(iv)
Eliminate d using eqn III & iv
2x+1-d=0...×2
6x-4-2d=0..×1
= 4x+2-2d=0
- 6x-4-2d=0
= -2x+6=0
-2x=-6
Divide both side by -2
X=3
Add xto eqn iv
6(3)-4-2d=0
18-4-2d=0
18-4=2d
14=2d
Divide both side by 2
7=d
- since T1=3
: Tn=3+ (10-1)7
= 3+9×7
= 3+63
=67.

Thanks 😊☺️😘

don't understand either

Grace

The first three terms of an A.P are 1,(3×+1) and (7×-4). find the 10th term