Advertisements
Advertisements
प्रश्न
Show that a1, a2,..., an... form an AP where an is defined as below:
an = 9 − 5n
Also, find the sum of the first 15 terms.
Advertisements
उत्तर
an = 9 − 5n
a1 = 9 − 5 × 1
= 9 − 5
= 4
a2 = 9 − 5 × 2
= 9 − 10
= −1
a3 = 9 − 5 × 3
= 9 − 15
= −6
a4 = 9 − 5 × 4
= 9 − 20
= −11
It can be observed that
a2 − a1 = −1 − 4 = −5
a3 − a2 = −6 − (−1) = −5
a4 − a3 = −11 − (−6) = −5
i.e., ak + 1 − ak is same every time. Therefore, this is an A.P. with common difference as −5 and first term as 4.
`S_n = n/2 [2a + (n - 1)d]`
`S_15 = 15/2 [2(4) + (15 - 1) (-5)]`
= `15/2 [8 + 14(-5)]`
= `15/2 (8 - 70)`
= `15/2 (-62)`
= 15 × (-31)
= -465
APPEARS IN
संबंधित प्रश्न
In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato and other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line.
A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?
[Hint: to pick up the first potato and the second potato, the total distance (in metres) run by a competitor is 2 × 5 + 2 ×(5 + 3)]
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
If the pth term of an AP is q and its qth term is p then show that its (p + q)th term is zero
Find the value of x for which (x + 2), 2x, ()2x + 3) are three consecutive terms of an AP.
If an denotes the nth term of the AP 2, 7, 12, 17, … find the value of (a30 - a20 ).
Find the sum of first n even natural numbers.
Find the sum of the following Aps:
i) 2, 7, 12, 17, ……. to 19 terms .
If the ratio of sum of the first m and n terms of an AP is m2 : n2, show that the ratio of its mth and nth terms is (2m − 1) : (2n − 1) ?
Choose the correct alternative answer for the following question.
For an given A.P. a = 3.5, d = 0, n = 101, then tn = ....
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.
Write the sum of first n even natural numbers.
If Sn denote the sum of the first n terms of an A.P. If S2n = 3Sn, then S3n : Sn is equal to
Suppose three parts of 207 are (a − d), a , (a + d) such that , (a + d) >a > (a − d).
Q.4
Q.5
The sum of the first three numbers in an Arithmetic Progression is 18. If the product of the first and the third term is 5 times the common difference, find the three numbers.
In an A.P. a = 2 and d = 3, then find S12.
The students of a school decided to beautify the school on the Annual Day by fixing colourful flags on the straight passage of the school. They have 27 flags to be fixed at intervals of every 2 m. The flags are stored at the position of the middle most flag. Ruchi was given the responsibility of placing the flags. Ruchi kept her books where the flags were stored. She could carry only one flag at a time. How much distance did she cover in completing this job and returning back to collect her books? What is the maximum distance she travelled carrying a flag?
Find the sum of all odd numbers between 351 and 373.
