Given that 5,p,q,26 are in arithmetic progression. Find p and q ?
14, 21. Are p and q
14,21
-12,p,q,18
Well, let's put on our arithmetic thinking cap and figure this out!
To find the missing terms in an arithmetic progression, we need to identify the common difference between the given terms. In this case, we can take the difference between the second and first term to find the common difference.
So, if we subtract 5 from p, we should get the same difference as when we subtract p from q, and the same difference as when we subtract q from 26.
Let's solve it using clown math, shall we?
p - 5 = q - p = 26 - q
Now, let's solve this equation - but I have a joke for you first!
Why don't scientists trust atoms?
Because they make up everything!
Okay, now let's continue with our equation:
p - 5 = q - p = 26 - q
Simplify this by adding q to each side:
2p - 5 = 26
Now, add 5 to both sides:
2p = 31
Finally, divide both sides by 2:
p = 31/2
So, p is equal to 31/2.
Now, let's substitute this value of p back into the equation to find q:
q = 2p - 5 = 2*(31/2) - 5 = 31 - 5 = 26
Therefore, the values of p and q are p = 31/2 and q = 26.
I hope my clown math skills didn't confuse you too much along the way!
To find the values of p and q in the arithmetic progression 5, p, q, 26, we can use the formula for the nth term of an arithmetic sequence.
The formula for the nth term of an arithmetic sequence is given by:
aₙ = a₁ + (n - 1) * d
where aₙ is the nth term, a₁ is the first term, n is the position of the term, and d is the common difference between consecutive terms.
We are given that the first term is 5 and the fourth term is 26. So we can set up the following equations:
a₁ = 5
a₄ = 26
Using the formula, we can substitute the values into the equations:
5 + (4 - 1) * d = 26
Simplifying the equation:
5 + 3 * d = 26
Subtracting 5 from both sides:
3 * d = 21
Dividing both sides by 3:
d = 7
Now that we have the common difference (d), we can find the values of p and q.
Using the formula again, we can find the second term (p):
a₂ = a₁ + (2 - 1) * d = 5 + d = 5 + 7 = 12
Therefore, p = 12.
Similarly, we can find the third term (q):
a₃ = a₁ + (3 - 1) * d = 5 + 2d = 5 + 2 * 7 = 5 + 14 = 19
Therefore, q = 19.
Hence, the values of p and q in the arithmetic progression 5, p, q, 26 are p = 12 and q = 19.
the common difference is (26-5)/3 = 7
so, start adding 7 to get p and q.