if the nth term of AP is 4n-10 .Find the value of 21 term and 50 term
Answers
Answer:
i) The first term of AP is -6.
ii) The common difference is 4.
iii) The 16th term is 54.
Step-by-step explanation:
Given : The nth term of a progression is (4n-10).
To find : Show that it is an AP and find its (i) first term, (ii) common difference (iii) 16 the term.
Solution :
The nth term of a progression is a_n=4n-10a
n
=4n−10
In order to check whether it an AP or not,
we find some terms by substituting random values of n.
For n = 1
\begin{gathered}a_1=4(1)-10\\a_1=-6\end{gathered}
a
1
=4(1)−10
a
1
=−6
For n =2
\begin{gathered}a_2=4(2)-10\\a_2=-2\end{gathered}
a
2
=4(2)−10
a
2
=−2
For n =3
\begin{gathered}a_3=4(3)-10\\a_3=2\end{gathered}
a
3
=4(3)−10
a
3
=2
The sequence is -10,-6,-2,2......
The difference of two consecutive terms should be equal in case of AP.
\begin{gathered}-2-(-6)=-2+6=4\\2-(-2)=2+2=4\end{gathered}
−2−(−6)=−2+6=4
2−(−2)=2+2=4
We can see the difference is equal.
So, it is an AP.
i) The first term of AP is -6.
ii) The common difference is 4.
iii) The 16th term is
a_{16}=4(16)-10=64-10=54a
16
=4(16)−10=64−10=54
#Learn more
If the nth term of a progression is (4n-10), show that it is an AP. Find is first term?
https://brainly.in/question/3846555
Step-by-step explanation: