Advertisements
Advertisements
प्रश्न
In an A.P. the 10th term is 46 sum of the 5th and 7th term is 52. Find the A.P.
Advertisements
उत्तर
It is given that,
t10 = 46
t5 + t7 = 52
Now,
\[t_n = a + \left( n - 1 \right)d\]
\[ t_{10} = a + \left( 10 - 1 \right)d\]
\[ \Rightarrow 46 = a + 9d\]
\[ \Rightarrow a = 46 - 9d . . . \left( 1 \right)\]
\[ t_5 + t_7 = 52\]
\[ \Rightarrow \left( a + \left( 5 - 1 \right)d \right) + \left( a + \left( 7 - 1 \right)d \right) = 52\]
\[ \Rightarrow a + 4d + a + 6d = 52\]
\[ \Rightarrow 2a + 10d = 52\]
\[ \Rightarrow 2\left( 46 - 9d \right) + 10d = 52 \left( \text { from }\left( 1 \right) \right)\]
\[ \Rightarrow 92 - 18d + 10d = 52\]
\[ \Rightarrow 92 - 8d = 52\]
\[ \Rightarrow 8d = 92 - 52\]
\[ \Rightarrow 8d = 40\]
\[ \Rightarrow d = 5\]
\[ \Rightarrow a = 46 - 9\left( 5 \right) \left( \text { from }\left( 1 \right) \right)\]
\[ \Rightarrow a = 46 - 45\]
\[ \Rightarrow a = 1\]
Hence, the given A.P. is 1, 6, 11, 16, ....
APPEARS IN
संबंधित प्रश्न
Find the 20th term from the last term of the A.P. 3, 8, 13, …, 253.
Find the sum of the following APs.
0.6, 1.7, 2.8, …….., to 100 terms.
Find the sum of the first 25 terms of an A.P. whose nth term is given by an = 7 − 3n
Find the sum of the first 22 terms of the A.P. : 8, 3, –2, ………
The sum of n natural numbers is 5n2 + 4n. Find its 8th term.
Is -150 a term of the AP 11, 8, 5, 2, ……?
The 9th term of an AP is -32 and the sum of its 11th and 13th terms is -94. Find the common difference of the AP.
In a flower bed, there are 43 rose plants in the first row, 41 in second, 39 in the third, and so on. There are 11 rose plants in the last row. How many rows are there in the flower bed?
Write an A.P. whose first term is a and common difference is d in the following.
a = 6, d = –3
The 9th term of an A.P. is equal to 6 times its second term. If its 5th term is 22, find the A.P.
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
Let Sn denote the sum of n terms of an A.P. whose first term is a. If the common difference d is given by d = Sn − kSn−1 + Sn−2, then k =
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 \[\frac{S_1}{S_2} =\]
The first three terms of an A.P. respectively are 3y − 1, 3y + 5 and 5y + 1. Then, y equals
A manufacturer of TV sets produces 600 units in the third year and 700 units in the 7th year. Assuming that the production increases uniformly by a fixed number every year, find:
- the production in the first year.
- the production in the 10th year.
- the total production in 7 years.
Q.19
Q.20
The sum of the first 2n terms of the AP: 2, 5, 8, …. is equal to sum of the first n terms of the AP: 57, 59, 61, … then n is equal to ______.
Solve the equation:
– 4 + (–1) + 2 + 5 + ... + x = 437
An Arithmetic Progression (A.P.) has 3 as its first term. The sum of the first 8 terms is twice the sum of the first 5 terms. Find the common difference of the A.P.
