Let Sn denote the sum of first n terms of an arithmetic progression. If S20 = 790 and S10 = 145, then S15

Engineering

Mathematics

Arithmetic Progression and Its Properties

Question

Let S_n denote the sum of first n terms of an arithmetic progression. If S₂₀ = 790 and S₁₀ = 145, then S₁₅ – S₅ is :

395

410

405

390

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S_{20} = \frac{20}{2} (2 a + 19 d) = 790 \Rightarrow 2 a + 19 d = 79

S_{10} = \frac{10}{2} (2 a + 9 d) = 145 \Rightarrow 2 a + 9 d = 29

10 d = 50

d = 5

S_{15} - S_{5} = \frac{15}{2} (2 a + 14 d) - \frac{5}{2} (2 a + 4 d)

10a + 95d = 395