Question

Find the 5th term, 10th term, and 100th term for the following sequence 5,3.9,2.8,1.7

Answer 1

Answer:

$\huge\frak\red{5th = 0.6} \\ \huge\frak\blue{10th = - 4.9} \\ \huge \frak\green{100th = - 103.9}$

Step-by-step explanation:

Given -

A. P. (Arithmetic Progression) = 5, 3.9, 2.8, 1.7....

To find -

The 5th, 10th and 100th term of A.P.

Solution -

here

$a_{1} = 5 \\ a_{2} = 3.9 \\ so \: common \: difference(d) = a_{2} - a_{1} \\ = 3.9 - 5 \\ = - 1.1$

First we will find the 5th term

$a_{n} = a_{1} + (n - 1)d \\ = > 5th = 5 + (5 - 1) \times - 1.1 \\ = > 5th = 5 + (4 \times - 1.1) \\ = > 5th = 5 + ( - 4.4) \\ = > 5th = 5 - 4.4 \\ = > 5th = 0.6$

Now will find the 10th term

$a_{n} = a_{1} + (n - 1)d \\ = > 10th = 5 + (10 - 1) \times - 1.1 \\ = > 10th = 5 + (9 \times - 1.1) \\ = > 10th = 5 + ( - 9.9) \\ = > 10th = 5 - 9.9 \\ = > 10th = - 4.9$

Then 100th term

$a_{n} = a_{1} + (n - 1)d \\ = > 100th = 5 + (100 - 1) \times - 1.1 \\ = > 100th = 5 + (99 \times - 1.1) \\ = > 100th = 5 + ( - 108.9) \\ = > 100th = 5 - 108.9 \\ = > 100th = 103.9$

Hence 5th term = 0.6

10th term = -4.9

100th term = -103.9

hope it helps.