मराठी

In an A.P, the First Term is 2 and the Sum of the First Five Terms is One-fourth of the Next Five Terms. Show that 20th Term is –112.

Advertisements
Advertisements

प्रश्न

In an A.P, the first term is 2 and the sum of the first five terms is one-fourth of the next five terms. Show that 20th term is –112.

Advertisements

उत्तर

First term = 2

Let d be the common difference of the A.P.

Therefore, the A.P. is 2, 2 + d, 2 + 2d, 2 + 3d, …

Sum of first five terms = 10 + 10d

Sum of next five terms = 10 + 35d

According to the given condition,

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

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Sum of the first p, q and r terms of an A.P. are a, b and c, respectively.

Prove that `a/p (q - r) + b/q (r- p) + c/r (p - q) = 0`


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)


Let < an > be a sequence. Write the first five term in the following:

a1 = a2 = 2, an = a− 1 − 1, n > 2


Show that the following sequence is an A.P. Also find the common difference and write 3 more terms in case.

 3, −1, −5, −9 ...


Show that the following sequence is an A.P. Also find the common difference and write 3 more terms in case.

−1, 1/4, 3/2, 11/4, ...


Find: 

18th term of the A.P.

\[\sqrt{2}, 3\sqrt{2}, 5\sqrt{2},\]


Which term of the sequence 12 + 8i, 11 + 6i, 10 + 4i, ... is purely real ?


How many terms are there in the A.P. 7, 10, 13, ... 43 ?


The 6th and 17th terms of an A.P. are 19 and 41 respectively, find the 40th term.


If 10 times the 10th term of an A.P. is equal to 15 times the 15th term, show that 25th term of the A.P. is zero.


If (m + 1)th term of an A.P. is twice the (n + 1)th term, prove that (3m + 1)th term is twice the (m + n + 1)th term.


Find the second term and nth term of an A.P. whose 6th term is 12 and the 8th term is 22.


The first and the last terms of an A.P. are a and l respectively. Show that the sum of nthterm from the beginning and nth term from the end is a + l.


Find the sum of all integers between 50 and 500 which are divisible by 7.


Solve: 

1 + 4 + 7 + 10 + ... + x = 590.


How many terms are there in the A.P. whose first and fifth terms are −14 and 2 respectively and the sum of the terms is 40?


How many terms of the A.P. −6, \[- \frac{11}{2}\], −5, ... are needed to give the sum −25?


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

 bc, ca, ab are in A.P.


If a, b, c is in A.P., prove that:

 (a − c)2 = 4 (a − b) (b − c)


If x, y, z are in A.P. and A1 is the A.M. of x and y and A2 is the A.M. of y and z, then prove that the A.M. of A1 and A2 is y.


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?


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.


In a potato race 20 potatoes are placed in a line at intervals of 4 meters with the first potato 24 metres from the starting point. A contestant is required to bring the potatoes back to the starting place one at a time. How far would he run in bringing back all the potatoes?


A man saved ₹66000 in 20 years. In each succeeding year after the first year he saved ₹200 more than what he saved in the previous year. How much did he save in the first year?


If the sum of n terms of an AP is 2n2 + 3n, then write its nth term.


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 \[\frac{3 + 5 + 7 + . . . + \text { upto n terms }}{5 + 8 + 11 + . . . . \text { upto 10 terms }}\] 7, then find the value of n.


If m th term of an A.P. is n and nth term is m, then write its pth term.


In n A.M.'s are introduced between 3 and 17 such that the ratio of the last mean to the first mean is 3 : 1, then the value of n is


The first and last terms of an A.P. are 1 and 11. If the sum of its terms is 36, then the number of terms will be


If the sum of n terms of an A.P., is 3 n2 + 5 n then which of its terms is 164?


If abc are in G.P. and a1/b1/y = c1/z, then xyz are in


The pth term of an A.P. is a and qth term is b. Prove that the sum of its (p + q) terms is `(p + q)/2[a + b + (a - b)/(p - q)]`.


Show that (x2 + xy + y2), (z2 + xz + x2) and (y2 + yz + z2) are consecutive terms of an A.P., if x, y and z are in A.P.


If 9 times the 9th term of an A.P. is equal to 13 times the 13th term, then the 22nd term of the A.P. is ______.


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


Let 3, 6, 9, 12 ....... upto 78 terms and 5, 9, 13, 17 ...... upto 59 be two series. Then, the sum of the terms common to both the series is equal to ______.


If a1, a2, a3, .......... are an A.P. such that a1 + a5 + a10 + a15 + a20 + a24 = 225, then a1 + a2 + a3 + ...... + a23 + a24 is equal to ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×