Notifications
Clear all
The sum of 4th and 8th terms of an A.P. is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the A.P.
Arithmetic Progressions
1
Posts
2
Users
0
Likes
314
Views
0
01/06/2021 10:54 am
Topic starter
The sum of 4th and 8th terms of an A.P. is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the A.P.
Answer
Add a comment
Add a comment
Topic Tags
1 Answer
0
01/06/2021 10:57 am
We know that, the nth term of the AP is;
an = a+(n-1)d
a4 = a+(4-1)d
a4 = a+3d
In the same way, we can write,
a8 = a+7d
a6 = a+5d
a10 = a+9d
Given that,
a4+a8 = 24
a+3d+a+7d = 24
2a+10d = 24
a+5d = 12 ………………… (i)
a6+a10 = 44
a +5d+a+9d = 44
2a+14d = 44
a+7d = 22 …………….. (ii)
On subtracting equation (i) from (ii), we get,
2d = 22 - 12
2d = 10
d = 5
From equation (i), we get,
a+5d = 12
a+5(5) = 12
a+25 = 12
a = -13
a2 = a+d
= -13+5 = -8
a3 = a2+d
= -8+5 = -3
Therefore, the first three terms of this A.P. are -13, -8, and -3.
Add a comment
Add a comment
Forum Jump:
Related Topics
-
A small terrace at a football ground comprises of 15 steps each of which is 50 m long and built of solid concrete. Each step has a rise of 1/4 m and a tread of 1/2 m.
4 years ago
-
The houses of a row are numbered consecutively from 1 to 49. Show that there is a value of x such that the sum of the numbers of the houses preceding the house numbered x is equal to the sum of the numbers of the houses following it.
4 years ago
-
A ladder has rungs 25 cm apart. figure. The rungs decrease uniformly in length from 45 cm at the bottom to 25 cm at the top.
4 years ago
-
The sum of the third and the seventh terms of an AP is 6 and their product is 8. Find the sum of first sixteen terms of the AP.
4 years ago
-
Which term of the AP: 121, 117, 113, . . ., is its first negative term? [Hint: Find n for an < 0]
4 years ago
Forum Information
- 321 Forums
- 27.3 K Topics
- 53.8 K Posts
- 72 Online
- 12.4 K Members
Our newest member: Stripchat
Forum Icons:
Forum contains no unread posts
Forum contains unread posts
Topic Icons:
Not Replied
Replied
Active
Hot
Sticky
Unapproved
Solved
Private
Closed