Answer:
Value of x = 3 in the given AP sequence.
Fourth term in the sequence is 19.
Step-by-step explanation:
Here, the given sequence is x+4, 2x+5, and 4x+3
So, the First term a = x + 4
Second Term b = 2x + 5
Third Term = 4x + 3
Now, as the given sequence is in AP.
⇒ b-a = c -b = Common Difference
⇒( 2x+5) - (x+4) = (4x+3) - (2x+5)
or, 2x + 5 - x - 4 = 4x + 3 - 2x -5
or, x + 1 = 2x - 2
or, -x = -3, or x = 3
So, the value of x = 3 in the given AP sequence.
⇒ First term = 3+ 4 = 7
⇒ Second term = 2(3) + 5 = 11
So, the Common Difference = Second term - First term
= 11 - 7 = 4
Now, Fourth term in an AP = Third term + Common Difference
= 4x + 3 + = 4x + 7 = 4(3) + 7 = 19
So, the fourth term in the sequence is 19.
