मराठी

Find the Sum to N Terms of the Arithmetic Progression, Whose Kth Term is 5k + 1.

Advertisements
Advertisements

प्रश्न

Find the sum to n terms of the A.P., whose kth term is 5k + 1.

Advertisements

उत्तर

It is given that the kth term of the A.P. is 5k + 1.

kth term = ak = + (k – 1)d

∴ + (k – 1)d = 5k + 1

a + kd – d = 5k + 1

Comparing the coefficient of k, we obtain d = 5

– = 1

⇒ a – 5 = 1

⇒ a = 6

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

The ratio of the sums of m and n terms of an A.P. is m2n2. Show that the ratio of mth and nthterm is (2m – 1): (2n – 1)


Between 1 and 31, m numbers have been inserted in such a way that the resulting sequence is an A.P. and the ratio of 7th and (m – 1)th numbers is 5:9. Find the value of m.


The difference between any two consecutive interior angles of a polygon is 5°. If the smallest angle is 120°, find the number of the sides of the polygon.


Find the sum of all numbers between 200 and 400 which are divisible by 7.


The pthqth and rth terms of an A.P. are a, b, c respectively. Show that (q – r )a + (r – p )b + (p – q )c = 0


Find:

 10th term of the A.P. 1, 4, 7, 10, ...


Which term of the A.P. 4, 9, 14, ... is 254?


Is 302 a term of the A.P. 3, 8, 13, ...?


If 9th term of an A.P. is zero, prove that its 29th term is double the 19th term.


The sum of three numbers in A.P. is 12 and the sum of their cubes is 288. Find the numbers.


Find the sum of the following arithmetic progression :

3, 9/2, 6, 15/2, ... to 25 terms


Find the sum of the following serie:

 2 + 5 + 8 + ... + 182


Find the sum of all even integers between 101 and 999.


If Sn = n2 p and Sm = m2 p, m ≠ n, in an A.P., prove that Sp = p3.


The sums of first n terms of two A.P.'s are in the ratio (7n + 2) : (n + 4). Find the ratio of their 5th terms.


If \[\frac{1}{a}, \frac{1}{b}, \frac{1}{c}\] are in A.P., prove that:

a (b +c), b (c + a), c (a +b) are in A.P.


If a2, b2, c2 are in A.P., prove that \[\frac{a}{b + c}, \frac{b}{c + a}, \frac{c}{a + b}\] are in A.P.


If a, b, c is in A.P., prove that:

 (a − c)2 = 4 (a − b) (b − c)


A man saved Rs 16500 in ten years. In each year after the first he saved Rs 100 more than he did in the receding year. How much did he save in the first year?


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.


We know that the sum of the interior angles of a triangle is 180°. Show that the sums of the interior angles of polygons with 3, 4, 5, 6, ... sides form an arithmetic progression. Find the sum of the interior angles for a 21 sided polygon.


If log 2, log (2x − 1) and log (2x + 3) are in A.P., write the value of x.


Write the value of n for which n th terms of the A.P.s 3, 10, 17, ... and 63, 65, 67, .... are equal.


If Sn denotes the sum of first n terms of an A.P. < an > such that

\[\frac{S_m}{S_n} = \frac{m^2}{n^2}, \text { then }\frac{a_m}{a_n} =\]

If a1, a2, a3, .... an are in A.P. with common difference d, then the sum of the series sin d [cosec a1cosec a2 + cosec a1 cosec a3 + .... + cosec an − 1 cosec an] is


If four numbers in A.P. are such that their sum is 50 and the greatest number is 4 times the least, then the numbers are


If n arithmetic means are inserted between 1 and 31 such that the ratio of the first mean and nth mean is 3 : 29, then the value of n is


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


Mark the correct alternative in the following question:

\[\text { If in an A . P } . S_n = n^2 q \text { and } S_m = m^2 q, \text { where } S_r \text{ denotes the sum of r terms of the A . P  . , then }S_q \text { equals }\]


If abc are in A.P. and xyz are in G.P., then the value of xb − c yc − a za − b is


If for an arithmetic progression, 9 times nineth term is equal to 13 times thirteenth term, then value of twenty second term is ____________.


If a1, a2, ..., an are in A.P. with common difference d (where d ≠ 0); then the sum of the series sin d (cosec a1 cosec a2 + cosec a2 cosec a3 + ...+ cosec an–1 cosec an) is equal to cot a1 – cot an 


A man accepts a position with an initial salary of Rs 5200 per month. It is understood that he will receive an automatic increase of Rs 320 in the very next month and each month thereafter. Find his salary for the tenth month


If the sum of n terms of an A.P. is given by Sn = 3n + 2n2, then the common difference of the A.P. is ______.


If the sum of n terms of a sequence is quadratic expression then it always represents an A.P


If the ratio of the sum of n terms of two APs is 2n:(n + 1), then the ratio of their 8th terms is ______.


The sum of n terms of an AP is 3n2 + 5n. The number of term which equals 164 is ______.


If 100 times the 100th term of an A.P. with non zero common difference equals the 50 times its 50th term, then the 150th term of this A.P. is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×