Question

а15=11
S15=105
a1=?
d=?

Answer 1

a₁₅=11    S₁₅=105     a₁-?     d-?
a₁₅=a₁+14d=11
S₁₅=(a₁+a₁₅)*15/2=105
(a₁+11)*15/2=105  |×(2/15)
a₁+11=14
a₁=3
3+14d=11
14d=8  |÷14
d=4/7.
Ответ: a₁=3       d=4/7.

Answer 2

$105= \frac{a_1+11}{2} \cdot 15 \\ 7 = \frac{a_1+11}{2} \\ 14=a_1+11 \\ a_1=14-11 \\ a_1 = 3 \\ d = \frac{11-3}{15-1} = \frac{8}{14} = \frac{4}{7}$