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If the first and fifteen terms of A.P. are 8 and -48 respectively, obtain the progression​

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Answer:

8, 4, 0, -4, - 8, .........

Explanation:

The n the term of an AP is


a_(n) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 8 and a₁₅ = - 48, then

8 + 14d = - 48 ( subtract 8 from both sides )

14d = - 56 ( divide both sides by 14 )

d = - 4

To obtain the progression subtract 4 from each term, that is

8, 4, 0, - 4, - 8, ......

User Imbr
by
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4 votes

Answer:

8, 4, 0, -4, -8, -12, -16, -20,...

Explanation:

Arithmetic Progressions

The general term of an arithmetic progression (A.P.) is:


a_n=a_1+(n-1).r

Where:

a1 = First term

an = Term number n

n = Number of the term

r = Common difference

We are given: a1=8, and a15=-48, n=15. Calculate r:


\displaystyle r=(a_n-a_1)/(n-1)


\displaystyle r=(-48-8)/(15-1)


\displaystyle r=(-56)/(14)

r = -4

We can get the terms of the progression by subtracting 4 to the previous term.

Thus, the first terms of the progression are:

8, 4, 0, -4, -8, -12, -16, -20,...

User Larsiusprime
by
8.6k points

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