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August 2022
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Знайдіть перший член і різницю арифметичної прогресії (аn) якщо а2+а13=77 і а6+а15=107
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Lesben
A2=a1+d, a13=a1+12d, a6=a1+5d, a15=a1+14d
(an=a1+(n-1)d)
a2+a13=a1+d+a1+12d=2a1+13d=77
a6+a15=a1+5d+a1+14d=2a1+19d=107
2a1+13d=77
2a1+19d=107
2a1+19d-(2a1+13d)=107-77
6d=30, d=30/6, d=5
2a1+13d=77, 2a1=77-13d, 2a1=77-13.5=77-65=12,a1=6
a1=6, d=5
============
(a2=6+5=11, a13=6+60=66, a2+a13=11+66=77
a6=6+25=31, a15=6+70=76, a6+a15=31+76=107)
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Answers & Comments
(an=a1+(n-1)d)
a2+a13=a1+d+a1+12d=2a1+13d=77
a6+a15=a1+5d+a1+14d=2a1+19d=107
2a1+13d=77
2a1+19d=107
2a1+19d-(2a1+13d)=107-77
6d=30, d=30/6, d=5
2a1+13d=77, 2a1=77-13d, 2a1=77-13.5=77-65=12,a1=6
a1=6, d=5
============
(a2=6+5=11, a13=6+60=66, a2+a13=11+66=77
a6=6+25=31, a15=6+70=76, a6+a15=31+76=107)