Advertisements
Advertisements
प्रश्न
An A.P. consists of 60 terms. If the first and the last terms be 7 and 125 respectively, find 32nd term.
Advertisements
उत्तर
Given
\[a = 7, n = 60, l = 125\]
\[l = a + (n - 1)d\]
\[ \Rightarrow 125 = 7 + (60 - 1)d\]
\[ \Rightarrow 125 = 7 + 59d\]
\[ \Rightarrow 118 = 59d\]
\[ \Rightarrow 2 = d\]
\[a_{32} = a + \left( 32 - 1 \right)d\]
\[ = a + 31d \]
\[ = 7 + 31 \times 2 \]
\[ = 7 + 62 \]
\[ = 69\]
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 (pn + qn2), where p and q are constants, find the common difference.
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.
Let the sum of n, 2n, 3n terms of an A.P. be S1, S2 and S3, respectively, show that S3 = 3 (S2– S1)
A man deposited Rs 10000 in a bank at the rate of 5% simple interest annually. Find the amount in 15th year since he deposited the amount and also calculate the total amount after 20 years.
If the nth term an of a sequence is given by an = n2 − n + 1, write down its first five terms.
A sequence is defined by an = n3 − 6n2 + 11n − 6, n ϵ N. Show that the first three terms of the sequence are zero and all other terms are positive.
Which term of the A.P. 4, 9, 14, ... is 254?
Is 68 a term of the A.P. 7, 10, 13, ...?
The 6th and 17th terms of an A.P. are 19 and 41 respectively, find the 40th term.
Find the 12th term from the following arithmetic progression:
3, 8, 13, ..., 253
The 4th term of an A.P. is three times the first and the 7th term exceeds twice the third term by 1. Find the first term and the common difference.
Find the sum of the following serie:
2 + 5 + 8 + ... + 182
Find the sum of all natural numbers between 1 and 100, which are divisible by 2 or 5.
Show that the sum of all odd integers between 1 and 1000 which are divisible by 3 is 83667.
Find the sum of the series:
3 + 5 + 7 + 6 + 9 + 12 + 9 + 13 + 17 + ... to 3n terms.
Find the sum of all those integers between 100 and 800 each of which on division by 16 leaves the remainder 7.
Solve:
1 + 4 + 7 + 10 + ... + x = 590.
Find the sum of odd integers from 1 to 2001.
Find an A.P. in which the sum of any number of terms is always three times the squared number of these terms.
If a, b, c is in A.P., then show that:
a2 (b + c), b2 (c + a), c2 (a + b) are also 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.
A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and agrees to pay the balance in annual instalments of Rs 500 plus 12% interest on the unpaid amount. How much the tractor cost him?
Write the common difference of an A.P. whose nth term is xn + y.
Write the common difference of an A.P. the sum of whose first n terms is
If the sum of n terms of an AP is 2n2 + 3n, then write its nth 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
If a1, a2, a3, .... an are in A.P. with common difference d, then the sum of the series sin d [sec a1 sec a2 + sec a2 sec a3 + .... + sec an − 1 sec an], is
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
The first and last term of an A.P. are a and l respectively. If S is the sum of all the terms of the A.P. and the common difference is given by \[\frac{l^2 - a^2}{k - (l + a)}\] , then k =
If the first, second and last term of an A.P are a, b and 2a respectively, then its sum is
If, S1 is the sum of an arithmetic progression of 'n' odd number of terms and S2 the sum of the terms of the series in odd places, then \[\frac{S_1}{S_2}\] =
Write the quadratic equation the arithmetic and geometric means of whose roots are Aand G respectively.
If a, b, c are in G.P. and a1/x = b1/y = c1/z, then xyz are in
If a, b, c, d are four distinct positive quantities in A.P., then show that bc > ad
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
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 ______.
