Question

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

Answer 1

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, ......

Answer 2

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,...