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My name is Ann [436]
2 years ago
13

The third term of an arithmetic sequence is-8, and the sum of the first 10 terms of the sequence is -230. Find:

Mathematics
1 answer:
mixas84 [53]2 years ago
4 0

Answer:

The first term of the sequence is a = 4

The sum of the first 13 terms is -480

Step-by-step explanation:

Given that:

The third term is: a + 2d = - 8 --- (1)

The \  sum  \ of  \ the \  first \ 10  \ terms  \ is:

-230 = \dfrac{10}{2}[2a+ (10-1)d]

-230 =5[2a+ (9)d]

-230 = 10a + 45d

10a + 45d = -230     ----(2)

From (1) and (2)

a + 2d = - 8

10a + 45d = -230

From (1), let a = -8 - 2d

Replace, the value of a in (1) to equation (2)

10(-8 -2d) + 45d = -230

-80 -20d +45d =-230

25d = -230 + 80

25d = -150

d = -150/25

d = -6

From equation (1);

a + 2(-6) = -8

a -12 = -8

a = -8 + 12

a = 4

Thus,the first term of the sequence a = 4

The \  sum  \ of  \ the \  first \ 13  \ terms  \ is:

S_n = \dfrac{n}{2}[2a+(n-1)d]

S_n = \dfrac{13}{2}[2(4)+(13-1)*-6]

S_n =7.5 [8+(12)\times -6]

S_n =7.5 [8-72]

= -480

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