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Aneli [31]
3 years ago
11

Find the sum sn of the arithmetic sequence a7=14/3 d=-4/3 n=15

Mathematics
1 answer:
Dafna1 [17]3 years ago
6 0

Answer:

S_{15}= 50

Step-by-step explanation:

Given

a_7 = \frac{14}{3}

d = -\frac{4}{3}

n = 15

Required

The sum of n terms

First, we calculate the first term using:

a_n = a + (n - 1)d

Let n = 7

So, we have:

a_7 = a + (7 - 1)d

a_7 = a + 6d

Substitute a_7 = \frac{14}{3} and d = -\frac{4}{3}

\frac{14}{3} = a + 6*\frac{-4}{3}

\frac{14}{3} = a -8

Collect like terms

a =\frac{14}{3} +8

Take LCM and solve

a =\frac{14+24}{3}

a =\frac{38}{3}

The sum of n terms is then calculated as:

S_n = \frac{n}{2}(2a + (n - 1)d)

Where: n = 15

So, we have:

S_n = \frac{15}{2}(2*\frac{38}{3} + (15 - 1)*\frac{-4}{3})

S_n = \frac{15}{2}(2*\frac{38}{3} + 14 *\frac{-4}{3})

S_n = \frac{15}{2}(2*\frac{38}{3} - 14 *\frac{4}{3})

S_n = \frac{15}{2}(\frac{2*38}{3} - \frac{14 *4}{3})

Take LCM

S_n = \frac{15}{2}(\frac{2*38-14 *4}{3})

S_n = \frac{15}{2}(\frac{20}{3})

Open bracket

S_n = \frac{15*20}{2*3}

S_n = \frac{300}{6}

S_n = 50

Hence,

S_{15}= 50

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