Use the arithmetic sequence nth term formula to solve the following problem: The first, second, and the nth terms of an arithmetic sequence are 2, 6, and 58 respectively, find the value of n and For that value of n, what is the exact value of the sum of n

The nth term formula for an arithmetic sequence is given by: tn = a + (n - 1)d, where a is the first term, d is the common difference, and n is the term number. We know that the first term (a) is 2 and the second term is 6. Using these two terms, we can find the common difference (d): d = (6 - 2)/(2 - 1) = 4 Now, we can use the nth term formula with the third term (tn = 58): 58 = 2 + (n - 1)4 Simplifying this equation, we get: 56 = 4(n - 1) n - 1 = 14 n = 15 Therefore, the value of n is 15. To find the sum of the n terms, we can use the formula: Sn = (n/2)(a + tn), where Sn is the sum of n terms. We know that a = 2 and tn = 58, so: Sn = (15/2)(2 + 58) Sn = 15 x 30 Sn = 450 Therefore, the exact value of the sum of the 15 terms in the sequence is 450.