Two A.P.s have the same common difference. The first term of one of these is $-1$ and that of the other is $-8$. Then find the difference between their $4^{th}$ terms.
Given: Two A.P.s have the same common difference. The first term of one of these is $-1$ and that of the other is $-8$.
To do: To find the difference between their $4^{th}$ terms.
Solution:
Let $d$ be common difference of both A.P.
For $1^{st}$ A.P.-
First term, $a=-1$
$\therefore\ 4^{th}$ term, $a_4=a+( 4-1)d$
$a_4=-1+3d\ ..........\ ( i)$
For $2^{nd}$ A.P.-
First term, $a=-8$
Common difference$=d$
$\therefore\ 4^{th}$ term, $a_4=-8+( 4-1)d$
$\Rightarrow a_4=-8+3d\ ..........\ ( ii)$
Difference between the $4^{th}$ term of both A.P.$=-1+3d-( -8+3d)$
$=-1+3d+8-3d$
$=7$
Thus, the difference between the $4^{th}$ term of the both A.P. is $7$.
Related Articles
- Two A.P.s have the same common difference. The first term of one A.P. is 2 and that of the other is 7. The difference between their 10th terms is the same as the difference between their 21st terms, which is the same as the difference between any two corresponding terms. Why?
- Choose the correct answer from the given four options:Two APs 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(A) \( -1 \)(B) \( -8 \)(C) 7(D) \( -9 \)
- Two arithmetic progressions have the same common difference. If the first term of the first progression is 3 and that of the other is 8, then the difference between their \( 3 rd \) term is
- Two APs have the same common difference. The first term of one AP is 2 and that of the other is 7 . The difference between their \( 10^{\text {th }} \) terms is the same as the difference between their \( 21^{\text {st }} \) terms, which is the same as the difference between any two corresponding terms. Why?
- Two APs have the same common difference. The difference between their 100th terms is 100, what is the difference between their 1000th terms?
- Two arithmetic progressions have the same common difference. The difference between their 100th terms is 100, what is the difference between their 1000th terms?
- The sum of the first \( n \) terms of an AP whose first term is 8 and the common difference is 20 is equal to the sum of first \( 2 n \) terms of another AP whose first term is \( -30 \) and the common difference is 8 . Find \( n \).
- The sum of first $n$ terms of an A.P. whose first term is 8 and the common difference is 20 is equal to the sum of first $2n$ terms of another A.P. whose first term is $-30$ and common difference is 8. Find $n$.
- Find first term, common difference and $5^{th}$ term of the sequence which have the following $n^{th}$ term: $3n+7$.
- The first term of an A.P. is 2 and the last term is 50. The sum of all these terms is 442. Find the common difference.
- The $14^{th}$ term of an A.P. is twice its $8^{th}$ term. If its $6^{th}$ term is $-8$, then find the sum of its first $20$ terms.
- The first term of an AP is \( -5 \) and the last term is 45 . If the sum of the terms of the AP is 120 , then find the number of terms and the common difference.
- Find The first four terms of an AP, whose first term is $–2$ and the common difference is $–2$.
- The first term of an A.P. is 5, the common difference is 3 and the last term is 80; find the number of terms.
- If the ratio of the sum of the first n terms of two APs is $(7n + 1)$: $(4n + 27)$, then find the ratio of their 9$^{th}$ terms.
Kickstart Your Career
Get certified by completing the course
Get Started