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Answer :
Final answer:
Thus the first term a = 3, and the fourth term can be calculated using the formula a4 = a + 3d, which gives us a4 = 18.
Explanation:
The question asks for the calculations of the first and fourth terms of an Arithmetic Progression (AP) given the sums of the first three and first four terms.
To start, we employ the fact that the sum of the first n terms of an AP can be represented by the formula Sn = n/2[2a + (n - 1)d], where a is the first term, d is the common difference, and n is the number of terms. Given S3 = 21 and S4 = 51, we can set up two equations:
- For S3: 3/2[2a + 2d] = 21
- For S4: 2[2a + 3d] = 51
By solving these equations simultaneously, we deduce that a = 3 and d = 5.
Consequently, the first term a = 3, and the fourth term can be calculated using the formula a4 = a + 3d, which gives us a4 = 18.
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