insert 6 arithmetic means between 4 and 22/3
Answers
Answer:
Insert 4 arithmetic means between 3 and 23.
First term is t
1
=a=3
Sixth term is t
6
=a+5d=23
d=4
The other four terms are t
2
=a+d=3+4=7
t
3
=a+2d=3+2∗4=11
t
4
=a+3d=3+3∗4=15
t
5
=a+4d=3+4∗4=19
6 arithmetic means between 4 and 22/3 are 94/21 , 104/21 , 38/7 , 124/21 , 134/21 , 48/7
Given : Numbers 4 and 22/3
To Find : Insert 6 arithmetic means between 4 and 22/3
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
After inserting 6 arithmetic means between 4 and 22/3
There will be 8 terms in AP
n = 8
1st term a = 4
Last (8th term) = 22/3
Using aₙ = a + (n-1)d
=> 22/3 = 4 + (8 - 1)d
=> 10/3 = 7d
=> d = 10/21
6 arithmetic means
4 + 10/21 , 4 + 2 * 10/21 , 4 + 3 * 10/21 , 4 + 4 * 10/21 , 4 + 5 * 10/21 , 4 + 6 * 10/21
= 94/21 , 104/21 , 38/7 , 124/21 , 134/21 , 48/7
6 arithmetic means between 4 and 22/3 are 94/21 , 104/21 , 38/7 , 124/21 , 134/21 , 48/7
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