Advertisements
Advertisements
Question
The nth term of an AP is given by (−4n + 15). Find the sum of first 20 terms of this AP?
Advertisements
Solution
Given, an = − 4n + 15
∴ a1 = − 4 × 1 + 15 = − 4 + 15 = 11
a2 = − 4 × 2 + 15 = − 8 + 15 = 7
a3 = − 4 × 3 + 15 = − 12 + 15 = 3
a4 = − 4 × 4 + 15 = − 16 + 15 = −1
It can be observed that
a2 − a1 = 7 − 11 = −4
a3 − a2 = 3 − 7 = −4
a4 − a3 = − 1 − 3 = −4
i.e., ak + 1 − ak is same every time. Therefore, this is an A.P. with common difference as
−4 and first term as 11.
`S_n=n/2[2a+(n-1)d]`
`S_20=20/2[2(11)+(20-1)(-4)]`
`=10[22+19(-4)]`
`=10(20-76)`
`=10(-54)`
`=-540`
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 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.
Which term of the AP ` 5/6 , 1 , 1 1/6 , 1 1/3` , ................ is 3 ?
The 8th term of an AP is zero. Prove that its 38th term is triple its 18th term.
If (3y – 1), (3y + 5) and (5y + 1) are three consecutive terms of an AP then find the value of y.
The sum of three consecutive terms of an AP is 21 and the sum of the squares of these terms is 165. Find these terms
Find the first term and common difference for the A.P.
`1/4,3/4,5/4,7/4,...`
In an A.P. 19th term is 52 and 38th term is 128, find sum of first 56 terms.
Find the sum of n terms of the series \[\left( 4 - \frac{1}{n} \right) + \left( 4 - \frac{2}{n} \right) + \left( 4 - \frac{3}{n} \right) + . . . . . . . . . .\]
If the 10th term of an A.P. is 21 and the sum of its first 10 terms is 120, find its nth term.
The sum of first n terms of an A.P is 5n2 + 3n. If its mth terms is 168, find the value of m. Also, find the 20th term of this A.P.
If the first term of an A.P. is a and nth term is b, then its common difference is
The common difference of the A.P. is \[\frac{1}{2q}, \frac{1 - 2q}{2q}, \frac{1 - 4q}{2q}, . . .\] is
A manufacturer of TV sets produces 600 units in the third year and 700 units in the 7th year. Assuming that the production increases uniformly by a fixed number every year, find:
- the production in the first year.
- the production in the 10th year.
- the total production in 7 years.
If the third term of an A.P. is 1 and 6th term is – 11, find the sum of its first 32 terms.
In an A.P., the sum of its first n terms is 6n – n². Find is 25th term.
In an A.P. sum of three consecutive terms is 27 and their products is 504. Find the terms. (Assume that three consecutive terms in an A.P. are a – d, a, a + d.)
If the numbers n - 2, 4n - 1 and 5n + 2 are in AP, then the value of n is ______.
Which term of the Arithmetic Progression (A.P.) 15, 30, 45, 60...... is 300?
Hence find the sum of all the terms of the Arithmetic Progression (A.P.)
The nth term of an Arithmetic Progression (A.P.) is given by the relation Tn = 6(7 – n)..
Find:
- its first term and common difference
- sum of its first 25 terms
