The 5th and 10th terms of an A.P are 0 and 10 respectively. The 20th term is what??
the common difference is ... (10 - 0) / (10 - 5) = 2
20th term is 10th term plus 10 differences
Thanks
The 20th term of that A.P. is what? Oh, I know! It's definitely the 20th term! Ba dum tss! But in all seriousness, let's solve this. We know that the common difference between terms is the same, so let's find it.
The 10th term is 10, and the 5th term is 0. That means the common difference between terms is 10 - 0 = 10.
Now, we want to find the 20th term. Since the common difference is 10, we can calculate it using the formula:
20th term = 5th term + (20 - 5) * common difference
20th term = 0 + 15 * 10
20th term = 0 + 150
20th term = 150
So, the 20th term of the A.P. is 150. I hope my math skills made you smile!
To find the 20th term of an arithmetic progression (A.P.), we need to determine the common difference (d) first.
Given that the 5th term (a₅) is 0 and the 10th term (a₁₀) is 10, we can use the formula for the nth term of an A.P.:
aₙ = a + (n - 1)d
where a is the first term and d is the common difference.
Using the values a₅ = 0 and a₁₀ = 10, we can substitute them into the formula:
0 = a + (5 - 1)d ------(1)
10 = a + (10 - 1)d ------(2)
To eliminate a, subtract equation (1) from equation (2):
10 - 0 = (a + (10 - 1)d) - (a + (5 - 1)d)
10 = 9d
Now, solve for d:
d = 10/9
Now that we have the common difference (d = 10/9), we can find the 20th term (a₂₀) using the formula:
aₙ = a + (n - 1)d
Substitute n = 20 and d = 10/9 into the formula:
a₂₀ = a + (20 - 1)(10/9)
Simplifying:
a₂₀ = a + 19(10/9)
= a + 190/9
However, we need one more piece of information to solve for a.