मराठी

Find the sum of last ten terms of the AP: 8, 10, 12,.., 126. - Mathematics

Advertisements
Advertisements

प्रश्न

Find the sum of last ten terms of the AP: 8, 10, 12,.., 126.

बेरीज
Advertisements

उत्तर

For finding the sum of last ten terms, we write the given AP in reverse order.

i.e., 126, 124, 122,..., 12, 10, 8

Here, first term (a) = 126,

Common difference (d) = 124 – 126 = –2

∴ S10 = `10/2 [2a + (10 - 1)d]`   ...`[∵ S_n = n/2[2a + (n - 1)d]]`

= 5{2(126) + 9(–2)}

= 5(252 – 18)

= 5 × 234

= 1170

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 5: Arithematic Progressions - Exercise 5.3 [पृष्ठ ५४]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 10
पाठ 5 Arithematic Progressions
Exercise 5.3 | Q 30 | पृष्ठ ५४

संबंधित प्रश्‍न

Find the sum of the following arithmetic progressions 

`(x - y)^2,(x^2 + y^2), (x + y)^2,.... to n term`


Find the sum of the first 15 terms of each of the following sequences having the nth term as

yn = 9 − 5n


How many terms of the A.P. : 24, 21, 18, ................ must be taken so that their sum is 78?


The first and the last terms of an A.P. are 34 and 700 respectively. If the common difference is 18, how many terms are there and what is their sum?


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


If the sum of first n terms is  (3n+  5n), find its common difference.


The nth term of an AP is given by (−4n + 15). Find the sum of first 20 terms of this AP?


Find the sum of n terms of the series \[\left( 4 - \frac{1}{n} \right) + \left( 4 - \frac{2}{n} \right) + \left( 4 - \frac{3}{n} \right) + . . . . . . . . . .\]


There are 25 trees at equal distances of 5 metres in a line with a well, the distance of the well from the nearest tree being 10 metres. A gardener waters all the trees separately starting from the well and he returns to the well after watering each tree to get water for the next. Find the total distance the gardener will cover in order to water all the trees.


Write the sum of first n even natural numbers.

 

Write the expression of the common difference of an A.P. whose first term is a and nth term is b.


If the first, second and last term of an A.P. are ab and 2a respectively, its sum is


If Sn denote the sum of n terms of an A.P. with first term and common difference dsuch that \[\frac{Sx}{Skx}\]  is independent of x, then

 


How many terms of the series 18 + 15 + 12 + ........ when added together will give 45?


Find second and third terms of an A.P. whose first term is – 2 and the common difference is – 2.


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`.


Find the sum:

`(a - b)/(a + b) + (3a - 2b)/(a + b) + (5a - 3b)/(a + b) +` ... to 11 terms


If sum of first 6 terms of an AP is 36 and that of the first 16 terms is 256, find the sum of first 10 terms.


Find the value of a25 – a15 for the AP: 6, 9, 12, 15, ………..


Solve the equation:

– 4 + (–1) + 2 + 5 + ... + x = 437


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×