Question

Dertemine a soma dos 15 termos da P.A (26,39,...)

Answer 1

15º termo:

$a_1 = 26 \\ r = 13 \\ a_{15} = \,? \\ \\ a_n = a_1+(n-1)r \\ \\ a_{15} = 26 + (15-1)\cdot 13 \\ \\ a_{15} = 26 + 14\cdot 13 \\ \\ a_{15} = 26 + 182 \\ \\ \boxed{a_{15}= 208}$

Soma dos 15 primeiros termos:

$a_1 = 26 \\ a_{15} = 208 \\ n = 15 \\ \\ S_{15} = \frac{(a_1+a_{n})n}{2} \\ \\ S_{15} = \frac{(26+208)15}{2} \\ \\ S_{15} = \frac{234.15}{2} \\ \\ S_{15} = 117.15 \\ \\ \boxed{\boxed{S_{15} = 1755}}$