Advertisements
Advertisements
प्रश्न
If the 5th and 12th terms of an A.P. are 30 and 65 respectively, what is the sum of first 20 terms?
Advertisements
उत्तर
\[\text { We have }: \]
\[ a_5 = 30\]
\[ \Rightarrow a + \left( 5 - 1 \right)d = 30\]
\[ \Rightarrow a + 4d = 30 . . . (i)\]
\[\text { Also }, a_{12} = 65\]
\[ \Rightarrow a + \left( 12 - 1 \right)d = 65\]
\[ \Rightarrow a + 11d = 65 . . . . . (ii)\]
\[\text { Solving (i) and (ii), we get }: \]
\[7d = 35\]
\[ \Rightarrow d = 5\]
\[\text { Putting the value of d in (i), we get }: \]
\[a + 4 \times 5 = 30\]
\[ \Rightarrow a = 10\]
\[ \therefore S_{20} = \frac{20}{2}\left[ 2 \times 10 + (20 - 1) \times 5 \right]\]
\[ \Rightarrow S_{20} = 10\left[ 2 \times 10 + (20 - 1) \times 5 \right]\]
\[ \Rightarrow S_{20} = 1150\]
APPEARS IN
संबंधित प्रश्न
Find the sum of odd integers from 1 to 2001.
If the sum of n terms of an A.P. is 3n2 + 5n and its mth term is 164, 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.
The pth, qth and rth terms of an A.P. are a, b, c respectively. Show that (q – r )a + (r – p )b + (p – q )c = 0
if `a(1/b + 1/c), b(1/c+1/a), c(1/a+1/b)` are in A.P., prove that a, b, c are in A.P.
Let < an > be a sequence. Write the first five term in the following:
a1 = 1, an = an − 1 + 2, n ≥ 2
The nth term of a sequence is given by an = 2n + 7. Show that it is an A.P. Also, find its 7th term.
If the sequence < an > is an A.P., show that am +n +am − n = 2am.
Which term of the A.P. 4, 9, 14, ... is 254?
If the nth term of the A.P. 9, 7, 5, ... is same as the nth term of the A.P. 15, 12, 9, ... find n.
Find the 12th term from the following arithmetic progression:
3, 8, 13, ..., 253
How many numbers of two digit are divisible by 3?
The angles of a quadrilateral are in A.P. whose common difference is 10°. Find the angles.
Find the sum of the following arithmetic progression :
1, 3, 5, 7, ... to 12 terms
Find the sum of the following serie:
101 + 99 + 97 + ... + 47
Find the sum of all natural numbers between 1 and 100, which are divisible by 2 or 5.
Find the sum of all odd numbers between 100 and 200.
Find the sum of all integers between 84 and 719, which are multiples of 5.
Find the sum of all those integers between 100 and 800 each of which on division by 16 leaves the remainder 7.
Find the sum of odd integers from 1 to 2001.
If \[\frac{1}{a}, \frac{1}{b}, \frac{1}{c}\] are in A.P., prove that:
\[\frac{b + c}{a}, \frac{c + a}{b}, \frac{a + b}{c}\] are in A.P.
If a, b, c is in A.P., then show that:
b + c − a, c + a − b, a + b − c are in A.P.
If a, b, c is in A.P., then show that:
bc − a2, ca − b2, ab − c2 are in A.P.
If \[a\left( \frac{1}{b} + \frac{1}{c} \right), b\left( \frac{1}{c} + \frac{1}{a} \right), c\left( \frac{1}{a} + \frac{1}{b} \right)\] are in A.P., prove that a, b, c are in A.P.
A manufacturer of radio sets produced 600 units in the third year and 700 units in the seventh year. Assuming that the product increases uniformly by a fixed number every year, find (i) the production in the first year (ii) the total product in 7 years and (iii) the product in the 10th 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.
Write the common difference of an A.P. whose nth term is xn + y.
If the sum of n terms of an A.P. be 3 n2 − n and its common difference is 6, then its first term is
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 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
The product of three numbers in A.P. is 224, and the largest number is 7 times the smallest. Find the numbers
If the sum of p terms of an A.P. is q and the sum of q terms is p, show that the sum of p + q terms is – (p + q). Also, find the sum of first p – q terms (p > q).
If in an A.P., Sn = qn2 and Sm = qm2, where Sr denotes the sum of r terms of the A.P., then Sq equals ______.
