Advertisements
Advertisements
Question
If the sum of n terms of an A.P. is 3n2 + 5n then which of its terms is 164?
Options
26th
27th
28th
none of these.
Advertisements
Solution
Here, the sum of first n terms is given by the expression,
Sn = 3n2 + 5n
We need to find which term of the A.P. is 164.
Let us take 164 as the nth term
So we know that the nthterm of an A.P. is given by,
an = Sn - Sn-1
So,
164 = Sn - Sn-1
164 = 3n2 + 5n - [3(n-1)2 +5(n-1) ]
Using the property,
( a - b)2 = a2 + b2 - 2ab
We get,
164 = 3n2 + 5n - [3(n2 + 1 - 2n) + 5 ( n-1)]
164 = 3n2 + 5n - [3n2 + 3 - 6n + 5n - 5]
164 = 3n2 + 5n -(3n2 - n - 2)
164 = 3n2 + 5n - 3n2 + n + 2
164 = 6n + 2
Further solving for n, we get
6n = 164 - 2
`n = 162/6`
n = 27
Therefore, 164 is the 27th term of the given A.P.
APPEARS IN
RELATED QUESTIONS
Show that a1, a2,..., an... form an AP where an is defined as below:
an = 3 + 4n
Also, find the sum of the first 15 terms.
The sum of three terms of an A.P. is 21 and the product of the first and the third terms exceed the second term by 6, find three terms.
Find the sum of all integers between 100 and 550, which are divisible by 9.
How many two-digits numbers are divisible by 3?
The sum of first three terms of an AP is 48. If the product of first and second terms exceeds 4 times the third term by 12. Find the AP.
If the numbers a, 9, b, 25 from an AP, find a and b.
The nth term of an AP is given by (−4n + 15). Find the sum of first 20 terms of this AP?
In an A.P. 19th term is 52 and 38th term is 128, find sum of first 56 terms.
For what value of n, the nth terms of the arithmetic progressions 63, 65, 67, ... and 3, 10, 17, ... equal?
The sum of first n terms of an A.P. is 5n − n2. Find the nth term of this A.P.
In a school, students decided to plant 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 double of the class in which they are studying. If there are 1 to 12 classes in the school and each class has two sections, find how many trees were planted by the students.
The first term of an A.P. is p and its common difference is q. Find its 10th term.
In an AP. Sp = q, Sq = p and Sr denotes the sum of first r terms. Then, Sp+q is equal to
The 9th term of an A.P. is 449 and 449th term is 9. The term which is equal to zero is
Q.1
Q.11
Q.12
Find second and third terms of an A.P. whose first term is – 2 and the common difference is – 2.
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 the integers between 100 and 200 that are
- divisible by 9
- not divisible by 9
[Hint (ii) : These numbers will be : Total numbers – Total numbers divisible by 9]
