In an arithmetic progression, if S₄₀=1030 and S₁₂=57 , then S₃₀-S₁₀ is equal to :

Step-by-step solution

aligned & S₄₀=1030 40 2 [2 a+39 d]=1030 & 2 a+39 d= 103 2 ....(1) & S₁₂=57 12 2 [2 a+11 d]=57 & 2 a+11 d= 57 6 ...(2) aligned Equation (1) - equation (2) aligned & 28 d= 103 2 - 57 6 & 28 d= 309-57 6 aligned d= 3 2 a=- 7 2 S₃₀-S₁₀= 30 2 [2 a+29 d]- 10 2 [2 a+9 d]=15[2 a+29 d]-5[2 a+9 d]=5[6 a+87 d-2 a-9 d]=5[4 a+78 d]=5[-14+117]=515