Final answer:
To find S19 in an Arithmetic Progression (A.P.), use the formula S = (n/2)(2a + (n-1)d), where S is the sum of the terms, n is the number of terms, a is the first term, and d is the common difference. Given t10 = 17, first determine the common difference (d) and find the first term (a). Substituting those values, calculate S19.
Step-by-step explanation:
To find S19 in an Arithmetic Progression (A.P.) when t10 = 17, we need to find the sum of the first 19 terms of the sequence. The formula to find the sum of an A.P. is given by: S = (n/2)(2a + (n-1)d), where S is the sum of the terms, n is the number of terms, a is the first term, and d is the common difference. Since we are given t10 = 17, we can determine the first term, a, and the common difference, d.
Step 1: Determine the common difference (d) using the formula tn = a + (n-1)d. Given t10 = 17, we can substitute the values to get 17 = a + (10-1)d.
Step 2: Solve for a by substituting the value of d obtained in Step 1 into the equation and solving for a. Once we have a and d, we can use the formula for the sum of an A.P. to find S19 by substituting the values into the formula.