Question

3,7,11,........., T100
T100=?
S=?

Answer 1

$t_{1}=3+4*\boxed{0} \\ t_{2}=3+4*\boxed{1} \\ t_{3} =3+4*\boxed{2} \\ \\ Deci~ t_{n}=3+4(n-1). \\ t_{100}=3+4*99=\boxed{399}.$

$S=3+3+4*1+3+4*2+...+3+4*99= \\ ~~~=3*100+4(1+2+3+...+99)= \\ ~~~=300+4* \frac{99*100}{2}= \\ ~~~= 20100.$

Answer 2

numere din 4 in 4 
primul a = 3  , este pe  locul 1 
T₁₀₀ = 3 + 99 · 4 = 3 + 396= 399 
S₁₀₀ = ( 3 + 399 ) · 100 /2 = 402 · 50 = 20100