Find the 8 th term from the end of the A.P 7, 10, 13, …….., 184.
Answer
363k+ views
Hint: In the question, we are given the first term (a) and the last term (l) of the arithmetic
progression. Also, we can find the common difference (d) of this A.P. by subtracting first term from
the second term. Using the formula $l=a+\left( n-1 \right)d$, we can find the number of terms (n).
The 8 th term from the end will be the (n-8+1) th term from the start.
Before proceeding with the question, we must know all the formulas that will be required to solve
this question. Let us consider an arithmetic progression having it’s first term as ‘a’, last term as ‘l’,
common difference as ‘d’ and ‘n’ be the number of terms.
In arithmetic progressions, we have a formula,
$l=a+\left( n-1 \right)d.............\left( 1 \right)$
If we want to find r th term from the starting, it is given by the formula,
${{a}_{r}}=a+\left( r-1 \right)d............\left( 2 \right)$
Also, the r th term from the end will be the (n-r+1) th $...........\left( 3 \right)$ term from the starting.
In the question, we are given an A.P. 7, 10, 13, …….., 184. The common difference (d) of this A.P. will
be the difference of the first and the second term and is equal to $10-7=3$. Let us first find the
number of terms ‘n’ of this A.P.
Substituting $a=7,l=184,d=3$ in formula $\left( 1 \right)$, we get,
$\begin{align}
& 184=7+\left( n-1 \right)\left( 3 \right) \\
& \Rightarrow \left( n-1 \right)\left( 3 \right)=177 \\
& \Rightarrow \left( n-1 \right)=59 \\
& \Rightarrow n=60 \\
\end{align}$
In the question, we are asked to find the 8 th term from the end. Using formula $\left( 3 \right)$, the
8 th term from the end will be the (60-8+1) th i.e. 53 th term from the start. Substituting $a=7,d=3,r=53$
in formula $\left( 2 \right)$, the 53 th term from the start is,
$\begin{align}
& {{a}_{53}}=7+\left( 53-1 \right)\left( 3 \right) \\
& \Rightarrow {{a}_{53}}=7+\left( 52 \right)\left( 3 \right) \\
& \Rightarrow {{a}_{53}}=7+156 \\
& \Rightarrow {{a}_{53}}=163 \\
\end{align}$
Hence, the 8 th term from the end of the A.P. is 163.
Note: There is a possibility that one may commit a mistake while converting the number of from the end to the number of terms from the starting. To convert the r th term from the end, there is a possibility that one may use the formula (n-r) instead of the formula (n-r+1) where ‘n’ is the total number of terms in the A.P.
progression. Also, we can find the common difference (d) of this A.P. by subtracting first term from
the second term. Using the formula $l=a+\left( n-1 \right)d$, we can find the number of terms (n).
The 8 th term from the end will be the (n-8+1) th term from the start.
Before proceeding with the question, we must know all the formulas that will be required to solve
this question. Let us consider an arithmetic progression having it’s first term as ‘a’, last term as ‘l’,
common difference as ‘d’ and ‘n’ be the number of terms.
In arithmetic progressions, we have a formula,
$l=a+\left( n-1 \right)d.............\left( 1 \right)$
If we want to find r th term from the starting, it is given by the formula,
${{a}_{r}}=a+\left( r-1 \right)d............\left( 2 \right)$
Also, the r th term from the end will be the (n-r+1) th $...........\left( 3 \right)$ term from the starting.
In the question, we are given an A.P. 7, 10, 13, …….., 184. The common difference (d) of this A.P. will
be the difference of the first and the second term and is equal to $10-7=3$. Let us first find the
number of terms ‘n’ of this A.P.
Substituting $a=7,l=184,d=3$ in formula $\left( 1 \right)$, we get,
$\begin{align}
& 184=7+\left( n-1 \right)\left( 3 \right) \\
& \Rightarrow \left( n-1 \right)\left( 3 \right)=177 \\
& \Rightarrow \left( n-1 \right)=59 \\
& \Rightarrow n=60 \\
\end{align}$
In the question, we are asked to find the 8 th term from the end. Using formula $\left( 3 \right)$, the
8 th term from the end will be the (60-8+1) th i.e. 53 th term from the start. Substituting $a=7,d=3,r=53$
in formula $\left( 2 \right)$, the 53 th term from the start is,
$\begin{align}
& {{a}_{53}}=7+\left( 53-1 \right)\left( 3 \right) \\
& \Rightarrow {{a}_{53}}=7+\left( 52 \right)\left( 3 \right) \\
& \Rightarrow {{a}_{53}}=7+156 \\
& \Rightarrow {{a}_{53}}=163 \\
\end{align}$
Hence, the 8 th term from the end of the A.P. is 163.
Note: There is a possibility that one may commit a mistake while converting the number of from the end to the number of terms from the starting. To convert the r th term from the end, there is a possibility that one may use the formula (n-r) instead of the formula (n-r+1) where ‘n’ is the total number of terms in the A.P.
Last updated date: 27th Sep 2023
•
Total views: 363k
•
Views today: 9.63k
Recently Updated Pages
What do you mean by public facilities

Difference between hardware and software

Disadvantages of Advertising

10 Advantages and Disadvantages of Plastic

What do you mean by Endemic Species

What is the Botanical Name of Dog , Cat , Turmeric , Mushroom , Palm

Trending doubts
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

The equation xxx + 2 is satisfied when x is equal to class 10 maths CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Drive an expression for the electric field due to an class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

What is the past tense of read class 10 english CBSE
