The 7th term of an a.p is 1o greater than the 5th term if the 2nd term is 12 find the 10th term
a + 6d - (a + 4d) = 10
2d = 10
d = 5
a+d = 12
a + 5 = 12
a = 7
10th term = a + 9d = ......
The 7th term of an AP is 10 greater than the 5th term. If the second term is 12. Find the 10th term
Well, let's have some fun with this arithmetic progression problem.
If the 2nd term is 12, we can say that the common difference between consecutive terms is the difference between the 2nd and 1st terms. But since we don't know the 1st term, let's just call it "X".
Now, we know that the 7th term is 10 greater than the 5th term. So, using our common difference (let's call it "D"), we can write the equation:
5th term + D = 7th term
But wait! We also know that the 7th term is 10 greater than the 5th term. That means we can rewrite our equation as:
5th term + D = 5th term + 10
Now, let's simplify this equation:
D = 10
Since we know that the common difference "D" is 10, we can find the 10th term by using our formula for the nth term of an arithmetic progression:
nth term = 1st term + (n - 1) * D
So, substituting in the known values:
10th term = X + (10 - 1) * 10
10th term = X + 90
But, since X is unknown, we can't determine the 10th term. However, we can definitely say that it's X + 90. So, the 10th term is a mystery waiting to be solved!
Remember, math can be funny too. Keep smiling!
To find the 7th term of an arithmetic progression (AP), we need to note that the difference between each consecutive term is constant.
Let's denote the second term of the AP as 'a', and the common difference between terms as 'd'. Given that the second term, a2, is 12, we have:
a2 = a + d = 12
We can use this information to find the value of 'd':
d = 12 - a
Now, we can find the 5th term, a5, by substituting the value of 'd':
a5 = a + 4d = a + 4(12 - a) = a + 48 - 4a = 48 - 3a
The 7th term, a7, is 10 greater than the 5th term:
a7 = a5 + 10 = (48 - 3a) + 10 = 58 - 3a
Since we now have an expression for the 7th term, we can find the 10th term, a10:
a10 = a7 + 3d = (58 - 3a) + 3(12 - a) = 58 - 3a + 36 - 3a = 94 - 6a
Therefore, the 10th term of the arithmetic progression is 94 - 6a, where 'a' is the value of the second term.