For what value of n,are the n^{th} terms of t | vedclass

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

Question

(A) For the first $AP: 63, 65, 67, \ldots$Here,first term $a = 63$ and common difference $d = 65 - 63 = 2$.The $n^{th}$ term is $a_n = a + (n - 1)d =

Vedclass · Accepted Answer

$13$

Vedclass · Answer

(A) For the first $AP: 63, 65, 67, \ldots$Here,first term $a = 63$ and common difference $d = 65 - 63 = 2$.The $n^{th}$ term is $a_n = a + (n - 1)d = 63 + (n - 1)2 = 63 + 2n - 2 = 61 + 2n$.For the second $AP: 3, 10, 17, \ldots$Here,first term $a = 3$ and common difference $d = 10 - 3 = 7$.The $n^{th}$ term is $a_n = a + (n - 1)d = 3 + (n - 1)7 = 3 + 7n - 7 = 7n - 4$.Given that the $n^{th}$ terms are equal:$61 + 2n = 7n - 4$$61 + 4 = 7n - 2n$$65 = 5n$$n = 13$.Thus,the $13^{th}$ terms of both $APs$ are equal.

For what value of $n$,are the $n^{th}$ terms of two $APs: 63, 65, 67, \ldots$ and $3, 10, 17, \ldots$ equal?

Similar Questions

In the following $APs,$ find the missing term in the box: $2, \square, 26$

Choose the correct choice in the following and justify: $30^{th}$ term of the $AP: 10, 7, 4, \ldots$ is

Write the first four terms of the $AP,$ when the first term $a$ and the common difference $d$ are given as follows: $a = 10, d = 10.$

In a flower bed,there are $23$ rose plants in the first row,$21$ in the second,$19$ in the third,and so on. There are $5$ rose plants in the last row. How many rows are there in the flower bed?

Find the number of terms in the following $AP$: $7, 13, 19, \ldots, 205$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module