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s344n2d4d5 [400]
3 years ago
8

The first term of an arithmetic progression is 80 and the common difference is -3. what is the greatest possible sum of the firs

t n terms of this sequence, and for which value of n does it occur?
I need help with this question, in advance thank you :)​
Mathematics
1 answer:
ikadub [295]3 years ago
5 0

Answer:

S=157

Step-by-step explanation:

an= a1+(n-1)d

a2=80+(2-1)(-3)

a2=80-3

a2=77

Sn=(a1+an)*n/2

S2=(80+a2)*2/2

S2=(80+77)*1

S2=157

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SOLUTION

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\begin{gathered} N=N_0e^{-kt} \\ where\text{ } \\ N_0=initial\text{ amount of C-14 at time t} \\ N=amount\text{ of C-14 at time t = 65\% of N}_0=0.65N_0 \\ k=0.0001 \\ t=time\text{ in years = ?} \end{gathered}

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\begin{gathered} N=N_0e^{-kt} \\ 0.65N_0=N_0e^{-0.0001t} \\ e^{-0.0001t}=\frac{0.65N_0}{N_0} \\ e^{-0.0001t}=0.65 \end{gathered}

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