A_n=a_1+(n-1)d
a_12=<span>a_1+33
S_12=(a_1+a_12)/2 * 12
Получаем систему уравнений:
</span>a_12=<span>a_1+33
</span>6a_1 + 6<span>a_12=210
</span><span>3a_1+3(a_1+33)=105
</span>a_1+<span>a_1+33=35
</span>2<span>a_1=2
</span><span>a_1=1
</span>a_12=1+33
<span>a_12=34</span>
4. 7^(1+log₇3)=7*7^log₇3=7*3=21.
6. a) log₀,₄35-log₀,₄14=log₀,₄(3/14)=log₂/₅(5/2)=log₂/₅(2/5)⁻¹=-1.
b) log₇0,5+log₇98=log₇(0,5*98)=log₇49=log₇7²=2.
Числа n и n+1
(n+n+1)²=(2n+1)²=n²+(n+1)²+264
4n²+4n+1=2n²+2n+264 2n²+2n-264=0
D=4+8*264= 2116 √D=46 n=1/4*[-2+46]=11
n=1/4[-2-46]=-12 не натуральное число.
ответ 11