Answer :
To find the sum of an arithmetic progression (AP), we need to know the first term, the last term, and the number of terms in the sequence.
In this problem, we're given:
- The first term (a) is 1.
- The last term (l) is 100.
- The number of terms (n) is 20.
The formula for the sum of an arithmetic progression is:
[tex]\[ \text{Sum} = \frac{n}{2} \times (a + l) \][/tex]
Let's break it down:
1. Identify the values:
- First term, [tex]\( a = 1 \)[/tex]
- Last term, [tex]\( l = 100 \)[/tex]
- Number of terms, [tex]\( n = 20 \)[/tex]
2. Plug the values into the formula:
[tex]\[ \text{Sum} = \frac{20}{2} \times (1 + 100) \][/tex]
3. Calculate the sum:
- First, calculate [tex]\( \frac{20}{2} \)[/tex] which equals 10.
- Next, add the first term and last term: [tex]\( 1 + 100 = 101 \)[/tex].
- Multiply the results: [tex]\( 10 \times 101 = 1010 \)[/tex].
So, the sum of the arithmetic progression is 1010.
In this problem, we're given:
- The first term (a) is 1.
- The last term (l) is 100.
- The number of terms (n) is 20.
The formula for the sum of an arithmetic progression is:
[tex]\[ \text{Sum} = \frac{n}{2} \times (a + l) \][/tex]
Let's break it down:
1. Identify the values:
- First term, [tex]\( a = 1 \)[/tex]
- Last term, [tex]\( l = 100 \)[/tex]
- Number of terms, [tex]\( n = 20 \)[/tex]
2. Plug the values into the formula:
[tex]\[ \text{Sum} = \frac{20}{2} \times (1 + 100) \][/tex]
3. Calculate the sum:
- First, calculate [tex]\( \frac{20}{2} \)[/tex] which equals 10.
- Next, add the first term and last term: [tex]\( 1 + 100 = 101 \)[/tex].
- Multiply the results: [tex]\( 10 \times 101 = 1010 \)[/tex].
So, the sum of the arithmetic progression is 1010.
