Advertisements
Advertisements
प्रश्न
The first and last terms of an AP are 17 and 350, respectively. If the common difference is 9, how many terms are there, and what is their sum?
Advertisements
उत्तर
Given that,
a = 17
l = 350
d = 9
Let there be n terms in the A.P.
l = a + (n − 1) d
350 = 17 + (n − 1)9
9n = 350 + 9 - 17
9n = 359 - 17
9n = 342
⇒ n = `342/9`
⇒ n = 38
Sn = `n/2(a+l)`
Sn = `38/2(17+350)`
= 19 × 367
= 6973
Thus, this A.P. contains 38 terms and the sum of the terms of this A.P. is 6973.
APPEARS IN
संबंधित प्रश्न
Find the sum of first 40 positive integers divisible by 6.
Which term of the progression 20, 19`1/4`,18`1/2`,17`3/4`, ... is the first negative term?
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 the following arithmetic progressions: 50, 46, 42, ... to 10 terms
Find the sum of the following arithmetic progressions:
1, 3, 5, 7, ... to 12 terms
Find the sum of the following arithmetic progressions:
`(x - y)/(x + y),(3x - 2y)/(x + y), (5x - 3y)/(x + y)`, .....to n terms
Find the sum of the first 40 positive integers divisible by 3
Find the sum 2 + 4 + 6 ... + 200
Find the sum of 28 terms of an A.P. whose nth term is 8n – 5.
Is -150 a term of the AP 11, 8, 5, 2, ……?
How many two-digit number are divisible by 6?
How many three-digit natural numbers are divisible by 9?
In an A.P., the first term is 22, nth term is −11 and the sum to first n terms is 66. Find n and d, the common difference
The sum of first seven terms of an A.P. is 182. If its 4th and the 17th terms are in the ratio 1 : 5, find the A.P.
The sum of the first n terms of an A.P. is 4n2 + 2n. Find the nth term of this A.P.
If the first, second and last term of an A.P. are a, b and 2a respectively, its sum is
The common difference of the A.P. \[\frac{1}{2b}, \frac{1 - 6b}{2b}, \frac{1 - 12b}{2b}, . . .\] is
If k, 2k − 1 and 2k + 1 are three consecutive terms of an A.P., the value of k is
Find the sum of first 10 terms of the A.P.
4 + 6 + 8 + .............
How many terms of the series 18 + 15 + 12 + ........ when added together will give 45?
Obtain the sum of the first 56 terms of an A.P. whose 18th and 39th terms are 52 and 148 respectively.
Find the sum of natural numbers between 1 to 140, which are divisible by 4.
Activity: Natural numbers between 1 to 140 divisible by 4 are, 4, 8, 12, 16,......, 136
Here d = 4, therefore this sequence is an A.P.
a = 4, d = 4, tn = 136, Sn = ?
tn = a + (n – 1)d
`square` = 4 + (n – 1) × 4
`square` = (n – 1) × 4
n = `square`
Now,
Sn = `"n"/2["a" + "t"_"n"]`
Sn = 17 × `square`
Sn = `square`
Therefore, the sum of natural numbers between 1 to 140, which are divisible by 4 is `square`.
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
The sum of the first 15 multiples of 8 is ______.
The sum of the first 2n terms of the AP: 2, 5, 8, …. is equal to sum of the first n terms of the AP: 57, 59, 61, … then n is equal to ______.
The famous mathematician associated with finding the sum of the first 100 natural numbers is ______.
Find the sum of first 'n' even natural numbers.
An Arithmetic Progression (A.P.) has 3 as its first term. The sum of the first 8 terms is twice the sum of the first 5 terms. Find the common difference of the A.P.
k + 2, 2k + 7 and 4k + 12 are the first three terms of an A.P. The first term of this A.P. is ______.
