8th term of an ap is 10 and common difference is 5 then find it's 19th term
please don't give me wrong answer then i will mark you
Share
8th term of an ap is 10 and common difference is 5 then find it's 19th term
please don't give me wrong answer then i will mark you
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Verified answer
Given :-
8th term of an AP is 10
common difference = 5
Required to find :-
Formula used :-
[tex]\huge{\dagger{\boxed{\tt{ {a}_{nth} = a + ( n - 1 ) d }}}}[/tex]
Solution :-
Given that :-
8th term of an AP = 10
Common difference ( d ) = 5
We need to find the 19th term of the arithmetic progession .
So,
In order to find the 19th term of the arithmetic progession we should find the first term of the sequence .
Hence,
8th term of the arithmetic progession can be written as ;
a + 7d = 10
However,
Common difference ( d ) = 5
So,
➦ a + 7d = 10
➦ a + 7 ( 5 ) = 10
➦ a + 35 = 10
➦ a = 10 - 35
➦ a = - 25
Hence,
The first term of the A.P is - 25
Similarly,
The values which we have are ;
First term ( a ) = - 25
Common difference (d ) = 5
Using the formula ,
[tex]\huge{\dagger{\boxed{\tt{ {a}_{nth} = a + ( n - 1 ) d }}}}[/tex]
here,
a = first term
d = common difference
n = the term number which you want to find
[tex]\rightarrow{\tt{ {a}_{nth} = {a}_{19} }}[/tex]
By substituting the values
[tex]\rightarrow{\tt{ {a}_{19} = - 25 + ( 19 - 1 ) 5 }}[/tex]
[tex]\rightarrow{\tt{ {a}_{19} = - 25 + ( 18 ) 5 }}[/tex]
[tex]\rightarrow{\tt{ {a}_{19} = - 25 + 90 }}[/tex]
[tex]\rightarrow{\tt{ {a}_{19} = 65 }}[/tex]
[tex]\huge{\dagger{\boxed{\sf{\therefore{ 19th \; term \; = \; 65 }}}}}[/tex]
Additional Information :-
1. The arithmetic sequence of the given one till 19th term is represented as ,
a = -25 , -20 , -15 , - - - - - - , 65
2. Formula for finding the sum of nth terms is
[tex]\large{\dagger{\boxed{\sf{ {s}_{nth} = \dfrac{n}{2} [ 2a + ( n - 1 ) d ] }}}}[/tex]
Given ,
The 8th term of an AP is 10 and the common difference is 5
We know that , the general formula of an AP is given by
[tex] \star \: \: \mathtt{ \fbox{ a_{n} = a + (n - 1)d}}[/tex]
Thus ,
[tex]\Rightarrow \sf 10 = a + (8 - 1)5 \\ \\ \Rightarrow \sf 10 = a + 35 \\ \\ \Rightarrow \sf a = - 25[/tex]
Now , we have to find the 19th term
Thus ,
[tex]\Rightarrow \sf a_{19} = - 25 + (19 - 1)5 \\ \\ \Rightarrow \sf a_{19} = - 25 + 90 \\ \\ \Rightarrow \sf a_{19} = 65[/tex]
[tex] \therefore \sf \bold{ \underline{The \: 19th \: term \: is \: 65 }}[/tex]