1. The problem statement, all variables and given/known data Let a1, a2, a3 denote the first three terms of a geometrical sequence, for which a1 + a2 + a3 = 26. a1 + 3, a2 + 4, a3 - 3 are the first three terms of an arithmetical sequence. Find the first term and the common quotient (ratio) of the geometrical sequence! 2. Relevant equations Arithmetical sequences: an = a1 + (n-1)d Sn = (n/2)(a1 + an) Geometric sequences: an = a1rn-1 Sn = a1 * ((r-1n)/(r-1)) 3. The attempt at a solution By taking the sum of the given arithmetical sequence: (a1 + a2 + a3) + 3 + 4 -3 = 26 +4 = 30 We know that: Sn = (n/2)(a1 + an) 30 = (3/2)(a1 + 3 + a3 - 3) > (3/2)(a1 + a3) 30 = (3/2)(20) Thus a1 + a3 = 20 Because of the given a1 + a2 + a3 = 26 This implies (a1 + a3) + a2 = 26 20 + a2 = 26 a2 = 6 Now, I found the second term of each sequence, however, I do not know how to go forward from this point. The four functions given for arithmetic and geometric sequences do not seem to help me any further because there are always two unknown variables!