The sixth term of an A.P. is 19 and its seven | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the first term of the $A.P.$ be $a$ and the common difference be $d$.The $n^{th}$ term of an $A.P.$ is given by $a_n = a + (n - 1)d$.Given,the

Vedclass · Accepted Answer

$107$

Vedclass · Answer

(B) Let the first term of the $A.P.$ be $a$ and the common difference be $d$.The $n^{th}$ term of an $A.P.$ is given by $a_n = a + (n - 1)d$.Given,the sixth term $a_6 = 19$,so $a + 5d = 19$ (Equation $1$).Given,the seventeenth term $a_{17} = 41$,so $a + 16d = 41$ (Equation $2$).Subtracting Equation $1$ from Equation $2$:$(a + 16d) - (a + 5d) = 41 - 19$$11d = 22$$d = 2$.Substituting $d = 2$ in Equation $1$:$a + 5(2) = 19$$a + 10 = 19$$a = 9$.Now,find the $50^{th}$ term $a_{50}$:$a_{50} = a + (50 - 1)d$$a_{50} = 9 + 49(2)$$a_{50} = 9 + 98 = 107$.

The sixth term of an $A.P.$ is $19$ and its seventeenth term is $41$. Find the $50^{th}$ term of the $A.P.$

Similar Questions

How many numbers lie between $10$ and $300,$ which when divided by $4$ leave a remainder $3?$

The $10^{th}$ and $20^{th}$ terms of an $A.P.$ are $73$ and $143$ respectively. Find the first term,the common difference,and the $30^{th}$ term of the $A.P.$

In an $AP$,if $d = -4$,$n = 7$,and $a_{n} = 4$,then $a$ is

There are $\ldots \ldots \ldots \ldots$ terms in the finite $A.P.$ $5, 10, 15, \ldots, 200$.

$A$ manufacturer of $TV$ sets produced $600$ sets in the third year and $700$ sets in the seventh year. Assuming that the production increases uniformly by a fixed number every year,find the production in the $10^{th}$ year.

Vedclass Test Series

Exam Paper Generator

Online Exam Module