How many terms are there in 20, 25, 30......140?
Created: 2 years ago |
Updated: 3 weeks ago
best des
To find the number of terms in the sequence 20, 25, 30, ..., 140, we can use the formula for the nth term of an arithmetic progression:
nth term (Tn) = a + (n - 1) * d
Where:
- a is the first term of the sequence (a = 20 in this case).
- d is the common difference between consecutive terms (d = 25 - 20 = 5 in this case).
- n is the number of terms we want to find.
We need to find the value of n when Tn is equal to 140, as that's the last term in the sequence.
140 = 20 + (n - 1) * 5
Now, solve for n:
140 - 20 = (n - 1) * 5 120 = (n - 1) * 5
Divide both sides by 5:
120/5 = (n - 1) 24 = n - 1
Now, add 1 to both sides:
n = 24 + 1 n = 25
So, there are 25 terms in the sequence 20, 25, 30, ..., 140. The correct answer is 25.
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