Question

Suma primilor 10 termeni ai unei progresii aritmetice
(an)unde a1= 3, a3 = 7​

Answer 1

Formula generală pentru o progresie aritmetică e:

$S = a_{1} + a_{2} + ... + a_{n} = \frac{n}{2}(a_{1}+a_{n})$

$a_{n} = a_{1} + r(n-1) \implies a_{3} = 3 + 2r = 7 \implies r = 2$

$a_{10} = 3 + 9 \cdot 2 = 3 + 18 = 21$

$S = a_{1} + a_{2} + ... + a_{10} = \frac{10}{2}(3 + 21) = \frac{10}{2}(24) = 10 \cdot 12 = \boxed{120}$

Answer 2

a₃=a₁+2r

7=3+2r

2r=4

r=2

a₁₉=a₁+9r

a₁₀=3+9×2

a₁₀=21

S₁₀=(a₁+a₁₀)/2×10

S₁₀=(3+21)/2×10

S₁₀=24/2×10

S₁₀=12×10

S₁₀=120