Two APs have the same common difference. The | vedclass

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

Question

(A) Let the first term of the first $AP$ be $a_1 = -1$ and the first term of the second $AP$ be $a_2 = -8$.Let the common difference for both $AP$s be

Vedclass · Accepted Answer

$7$

Vedclass · Answer

(A) Let the first term of the first $AP$ be $a_1 = -1$ and the first term of the second $AP$ be $a_2 = -8$.Let the common difference for both $AP$s be $d$.The $n^{	ext{th}}$ term of an $AP$ is given by $T_n = a + (n - 1)d$.The $4^{	ext{th}}$ term of the first $AP$ is $T_4 = a_1 + (4 - 1)d = -1 + 3d$.The $4^{	ext{th}}$ term of the second $AP$ is $T'_4 = a_2 + (4 - 1)d = -8 + 3d$.The difference between their $4^{	ext{th}}$ terms is $(a_1 + 3d) - (a_2 + 3d) = a_1 - a_2$.Substituting the values,we get $(-1) - (-8) = -1 + 8 = 7$.Thus,the difference between their $4^{	ext{th}}$ terms is $7$.

Two $AP$s have the same common difference. The first term of one of these is $-1$ and that of the other is $-8$. Then the difference between their $4^{\text{th}}$ terms is

Similar Questions

Determine whether the following sequence is an $A.P.$ or not. (Assume that the pattern continues.) If it is an $A.P.$,find its $n^{th}$ term: $1, 4, 9, 16, \ldots $

Find the sum of the series: $3 + 7 + 11 + \ldots + 119$.

Determine whether the following sequence is an $A.P.$ or not. (Assume that the pattern continues.) If it is an $A.P.$,find its $n^{th}$ term: $111, 107, 103, 99, \ldots$

In each of the following,$a$ and $d$ for an $A.P.$ are given. Find the $A.P.$ in each case. $a = 21, d = -7$.

Find the sum of the first $30$ terms of the $A.P.$ $15, 20, 25, \ldots$

Vedclass Test Series

Exam Paper Generator

Online Exam Module