If 9th term of an. A. P is zero prove that it's 29th term is double the 19th term.
Answers
Step-by-step explanation:
Given: 9th term of an A.P. is 0. Therefore,
We have to prove that
Thus,
And
From equation (2) and (3),
Hence proved
Show less
Related questions
0
votes
1
answer
If 9th term of an A.P. is zero , prove that its 29th term is double the 19th term .
asked Jan 8, 2018 in Class X Maths by priya12 (-11,283 points)
0
votes
1
answer
If the 9th term of an AP is zero, then prove that its 29th term is twice its 19th term.
asked Feb 10, 2018 in Class X Maths by aditya23 (-390 points)
arithmetic progressions
0
votes
1
answer
The sum of the first six terms of an A.P. is zero and the fourth term is 2. Find the sum of its first 30 terms.
asked Jan 8, 2018 in Class X Maths by priya12 (-11,283 points)
0
votes
1
answer
The first term of an A.P. is a and the sum of the first p terms is zero, show that the sum of its next q terms -a(p+q)q) / (p-1)
asked Feb 20, 2018 in Class XI Maths by nikita74 (-1,039 points)
sequence and series
0
votes
1
answer
If the sum of m terms of an A.P is the same as the sum of n terms of the same A.P, show that the sum of its (m+n) terms is zero.
asked Nov 7, 2017 in Class X Maths by aditya23 (-390 points)
+1
vote
0
answers
If a1, a2, a3, ........, an be an A.P. , of non zero terms, prove that
asked Sep 2, 2018 in Class XI Maths by manmeetkaur47 (16 points)
sequence and series
0
votes
1
answer
If the mth term of an A.P. be 1/n and nth term be 1/m, then show that its (mn)th term is 1.
asked Nov 7, 2017 in Class X Maths by aditya23 (-390 points)
0
votes
1
answer
If 9 times the 9th term of an A.P. is equal to 13 times the 13th term, then the 22nd term of the A.P. is
asked Feb 20, 2018 in Class XI Maths by vijay Premium (528 points)
sequence and series
0
votes
1
answer
In a certain A.P the 24th term is twice the 10th term. Prove that the 72nd term is twice the 34th term .
asked Jan 8, 2018 in Class X Maths by priya12 (-11,283 points)
0
votes
1
answer
If the sum of p terms of an A.P is 3p2 + 4p, find its nth term.
asked Jan 8, 2018 in Class X Maths by priya12 (-11,283 points)
Studyrankers
All categories
Biology (197)
Board Exams (163)
Class XII Business Studies (580)
Class XII Accountancy (17)
Class XII Economics (14)
Class XII Psychology (12)
Class XII Political Science (11)
Class XII Physical Education (8)
Class XII English (222)
Class XII Biology (754)
Class XII Chemistry (245)
Class XII Physics (355)
Class XII Maths (497)
Class XI Business Studies (1,281)
Class XI Accountancy (21)
Class XI Economics (29)
Class XI Psychology (5)
Class XI Political Science (55)
Class XI Physical Education (25)
Class XI English (55)
Class XI Biology (2,942)
Class XI Chemistry (418)
Class XI Physics (378)
Class XI Maths (505)
Class X Social Science (8,708)
Class X Science (4,329)
Class X Maths (1,707)
Class X English (1,045)
Class X Hindi (508)
Class X Computer (12)
Class IX Social Science (3,096)
Class IX Science (1,298)
Class IX Maths (1,668)
Class IX English (1,335)
Class IX Hindi (167)
Class IX Computer (28)
Class VIII Social Science (144)
Class VIII Science (811)
Class VIII Maths (346)
Class VIII English (37)
Class VIII Hindi (9)
Class VIII Computer (3)
Class VII Maths (335)
Class VII Science (249)
Class VII English (8)
Class VII Social Science (29)
Class VII Hindi (5)
Class VII Computer (4)
Class VI Maths (6)
Class VI Social Science (8)
Class VI Science (11)
Class VI English (2)
Class VI Hindi (3)
Class VI Computer (3)
Sanskrit (1)
Geography (13)
History (10)
Political Science (0)
Who is Who (0
Question:-
➡ If the 9th term of an A.P. is zero then prove that, 29th term is twice the 19th term.
Proof:-
Let us assume that,
➡ First term of the A.P. = a and,
➡ Common Difference = d
Now,
Nth term of an A.P. = a + (n -1)d
So,
9th term = a + (9 - 1)d
= a + 8d
Now, it's given that, 9th term of the A.P. is zero.
➡ a + 8d = 0 .....(i)
Now,
29th term = a + (29 - 1)d
= a + 28d
19th term = a + (19 - 1)d
= a + 18d
Now,
29th term - 2 × 19th term
= a + 28d - 2 × (a + 18d)
= a + 28d - 2a - 36d
= -a - 8d
= -1(a + 8d)
= -1 × 0
= 0
Hence,
29th term - 2 × 19th term = 0
➡ 29th term = 2 × 19th term. (Hence Proved)