Advertisements
Advertisements
Question
Find an AP whose 4th term is 9 and the sum of its 6th and 13th terms is 40.
Advertisements
Solution
Let a be the first term and d be the common difference of the AP. Then,
a4 = 9
⇒ a + (4-1) d = 9 [ an = a + (n-1) d]
⇒ a +3d = 9 ....................(1)
Now,
a6 +a13 = 40 (Given)
⇒ (a +5d ) + (a +12d) = 40
⇒ 2a + 17d = 40 ...............(2)
From (1) and (2), we get
2(9-3d ) +17d = 40
⇒ 18-6d + 17d = 40
⇒ 11d = 40 - 18 =22
⇒ d =2
Putting d = 2 in (1), we get
a +3 × 2 = 9
⇒ a = 9-6=3
Hence, the AP is 3, 5, 7, 9, 11,…….
APPEARS IN
RELATED QUESTIONS
The first and the last terms of an AP are 7 and 49 respectively. If sum of all its terms is 420, find its common difference.
In a school, students thought of planting trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant will be the same as the class, in which they are studying, e.g., a section of class I will plant 1 tree, a section of class II will plant 2 trees, and so on till class XII. There are three sections of each class. How many trees will be planted by the students?
If the sum of first m terms of an A.P. is the same as the sum of its first n terms, show that the sum of its first (m + n) terms is zero
Find the sum of all natural numbers between 250 and 1000 which are divisible by 9.
For an given A.P., t7 = 4, d = −4, then a = ______.
The Sum of first five multiples of 3 is ______.
Find the sum of all 2 - digit natural numbers divisible by 4.
If Sn denotes the sum of first n terms of an A.P., prove that S12 = 3(S8 − S4).
Write the sum of first n odd natural numbers.
The first term of an A.P. is p and its common difference is q. Find its 10th term.
Write the nth term of the \[A . P . \frac{1}{m}, \frac{1 + m}{m}, \frac{1 + 2m}{m}, . . . .\]
Sum of n terms of the series `sqrt2+sqrt8+sqrt18+sqrt32+....` is ______.
The common difference of an A.P., the sum of whose n terms is Sn, is
If the second term and the fourth term of an A.P. are 12 and 20 respectively, then find the sum of first 25 terms:
In an A.P. (with usual notations) : given a = 8, an = 62, Sn = 210, find n and d
Shubhankar invested in a national savings certificate scheme. In the first year he invested ₹ 500, in the second year ₹ 700, in the third year ₹ 900 and so on. Find the total amount that he invested in 12 years.
Find the sum of those integers between 1 and 500 which are multiples of 2 as well as of 5.
Find the sum of the integers between 100 and 200 that are not divisible by 9.
Find the sum of all odd numbers between 351 and 373.
