Step-by-step explanation:The third term of an A.P = 8 Ninth term of the A.P = 3 times the third term by 2Sum of FIRST 19 terms➟ We know that the third term of the A.P = 8     a₁ + 2d = 8 -----(1) ➟ ALSO by given we know that,     Ninth term of the A.P (a₉) = 3 × (Third term) + 2      a₉ = 3 × 8 + 2      a₉ = 24 + 2      a₉ = 26 ➟ Also,    a₁ + 8d = 26 ------(2) ➟ Solving equation 1 and equation 2 by elimination METHOD,    a₁ + 8d = 26    a₁ + 2d = 8           6d = 18             d = 18/6             d = 3 ➟ Hence common difference of the A.P is 3. ➟ Now substitute the value of d in equation 1,     a₁ + 2 × 3 = 8     a₁ + 6 = 8     a₁ = 8 - 6 =2 ➟ Hence first term of the A.P is 2 .➟ Now sum of terms of an A.P is given by,        where n = number of terms                a₁ = first term               d = common difference ➟ Substitute the given data,     S₁₉ = 19/2 ( 2 × 2 + (19 - 1) × 3)     S₁₉ = 9.5 × (4 + 54)     S₁₉ = 551 ➟ Hence the sum of 19 terms of the A.P is 551.