Question

2x+1,4x-1,5x+1,.........are in arithmetic sequence. write the sequence​

Answer 1

Solution :- We know a condition in A.P that 2b = a+c always satisfy .

Since, 2(4x-1 ) = 5x+1+2x+1

=>8x-2 = 7x+2

=> x = 4

a = 2*4+1 = 9

b = 4* 4 -1 = 15

c = 5*4 +1 = 21

9, 15 , 21 , 27 ...... are the sequence of this Arithamatic series .

Hope it's helpful

Answer 2

Answer:

The sequence is 9, 15, 21,...

Given:

• 2x + 1, 4x - 1, 5x + 1 are in the arithmetic progression.

To find:

• The sequence.

Solution:

=> $\sf{t_{1}}$ = 2x + 1,

=> $\sf{t_{2}}$ = 4x - 1,

=> $\sf{t_{3}}$ = 5x + 1

$\boxed{\sf{2\times \ t_{2}=t_{1}+t_{2}}}$

$\sf{\therefore}$ 2 (4x - 1) = 2x + 1 + 5x + 1

$\sf{\therefore}$ 8x - 2 = 7x + 2

$\sf{\therefore}$ x = 4

The sequence is 2(4) + 1, 4(4) - 1, 5(4) + 1,...

Therefore, the sequence is 9, 15, 21,...