Question

in the sequence 0.12,0.17,0.22, find n if the nth term is 67

Answer 1

Answer:

Given an arithmetic sequence 0.12,0.17,0.22,...0.12,0.17,0.22,... where the first term a1=0.12a

=0.12 . our goal is to find the 67th term a{67}

.

First thing to do is to find the common difference dd . Without solving, we can observe that the difference between 0.170.17 & 0.120.12 and 0.220.22 & 0.170.17 is 0.050.05 . We then say that d=0.05d=0.05 .

We can now plug in the values to the explicit formula an=a1(n-1)d

n=a1 +(n−1)d

a 67

$\begin{gathered}a_{67}=0.12+(67-1)(0.05)\\a_{67}=0.12+(66)(0.05)\\a_{67}=0.12+3.30\\a_{67}=3.42\end{gathered}$

Therefore, the 67th term of the sequence is 3.42

Answer 2

Given : sequence 0.12,0.17,0.22

nth term is 0.67

To Find :  n  

Solution:

Arithmetic sequence : Sequence of terms in which difference between one term and the next is a constant.

This is also called Arithmetic Progression AP

Arithmetic sequence can be represented in the form :

a, a + d  , a + 2d , …………………………, a + (n-1)d

a = First term

d = common difference = aₙ-aₙ₋₁

nth term =  aₙ =  a + (n-1)d  

Sₙ = (n/2)(2a + (n - 1)d)

sequence 0.12,0.17,0.22

d = 0.17 - 0.12 = 0.05    

0.22 - 0.17 = 0.05

a = 0.17

d = 0.05

nth  term  =0.67

0.67 = 0.17 + (n - 1)0.05

=> 0.5  = (n - 1)(0.05)

=> n - 1  =  10

=> n = 10 + 1

=>  n = 11

11th term is  0.67

Learn More:

In an infinite g.P. Each term is equal to three times the sum of all the ...

brainly.in/question/9079152

if s1,s2,s3...sp are the sum of infinite geometric series whose first ...

brainly.in/question/5796750

How to derive sum of n terms of an A.P? - Brainly.in

brainly.in/question/7849150

In an A.P if sum of its first n terms is 3n square +5n and it's Kth term ...

brainly.in/question/8236011