Answer :
Final answer:
The 4th term of an AP is 7 and the 21st term is 41. The common difference is 2, the first term is 1, and the sum of the first 20 terms is 400.
Explanation:
To solve this problem, we need to recall the formula for the nth term of an AP (Arithmetic Progression), which is expressed as an = a + (n - 1)d, where an is the nth term, a is the first term, d is the common difference, and n is the number of terms.
Using the information given that the 4th term of an AP is 7 and the 21st term is 41:
- 4th term: a + 3d = 7
- 21st term: a + 20d = 41
Subtracting the first equation from the second gives us:
17d = 34 → d = 2
So, the common difference (b) is 2. Now, substituting for d, we find the first term:
a + 3(2) = 7 → a = 1
Thus, the first term (a) of the AP is 1.
To find the sum of the first 20 terms (S20), we use the formula: Sn = n/2 [2a + (n - 1)d]. Substituting the values:
S20 = 20/2 [2(1) + (20 - 1)(2)]
S20 = 10 [2 + 38]
S20 = 10 [40] = 400
Therefore, the sum of the first 20 terms of the AP is 400.
Learn more about Arithmetic Progression here:
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