Question

Find the 15th term of arithmetic progressions :3,1,-1,-3 etc .

Answer 1

Answer:

-25

Step-by-step explanation:

a=3

d=-2

n term=15

an=a+(n-1)d

an=3+(15-1)-2

an=3+(14)-2

an=3-28

an=-25

Answer 2

Answer:

The 15th term of the given arithmetic progression is -25.

Step-by-step explanation:

Step : 1 The common difference of the arithmetic progression,

$\begin{aligned}d & =a_2-a_1 \\& =1-3 \\& =-2\end{aligned}$

The $n^{t h}$ term of the progression is given as,

$\begin{aligned}& a_{\mathbf{n}}=a_1+(\mathbf{n}-1) d \\& \Rightarrow a_{\mathrm{n}}=3+(n-1)(-2) \\& \Rightarrow a_{\mathrm{n}}=3-2(n-1)\end{aligned}$

Step : 2  The  15th term of the progression is given as,

n term=15

an=a+(n-1)d

an=3+(15-1)-2

an=3+(14)-2

an=3-28

an=-25

Step : 3 A succession of words with a common difference between them that has a constant value is known as an arithmetic progression. It is employed to generalise a collection of trends that we notice in daily life. As an illustration, AP is used to forecast any sequence, such as when a person is waiting for a cab. He or she can anticipate when the next taxi will arrive assuming that traffic is flowing at a steady speed.

Step : 4 An arithmetic progression is a set of integers with a fixed difference between any two succeeding numbers (A.P.). 3,6,9,12,15,18,and 21 are examples of A.P.

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