Advertisements
Advertisements
प्रश्न
Find four consecutive terms in an A.P. whose sum is 12 and sum of 3rd and 4th term is 14.
(Assume the four consecutive terms in A.P. are a – d, a, a + d, a +2d)
Advertisements
उत्तर
Assume that the four consecutive terms in A.P. are a – d, a, a + d, a +2d .
It is given that,
Sum of four consecutive terms = 12
Sum of 3rd and 4th term = 14
\[\left( a - d \right) + a + \left( a + d \right) + \left( a + 2d \right) = 12\]
\[ \Rightarrow 4a + 2d = 12\]
\[ \Rightarrow 2a + d = 6\]
\[ \Rightarrow 2a = 6 - d . . . \left( 1 \right)\]
\[\left( a + d \right) + \left( a + 2d \right) = 14\]
\[ \Rightarrow 2a + 3d = 14\]
\[ \Rightarrow 6 - d + 3d = 14\]
\[ \Rightarrow 2d = 14 - 6\]
\[ \Rightarrow 2d = 8\]
\[ \Rightarrow d = 4 \left( \text { from} \left( 1 \right) \right)\]
\[ \Rightarrow 2a = 6 - d\]
\[ \Rightarrow 2a = 6 - 4\]
\[ \Rightarrow 2a = 2\]
\[ \Rightarrow a = 1\]
Hence, the terms are –3, 1, 5 and 9.
APPEARS IN
संबंधित प्रश्न
If the sum of first m terms of an A.P. is the same as the sum of its first n terms, show that the sum of its first (m + n) terms is zero
Find the 12th term from the end of the following arithmetic progressions:
3, 5, 7, 9, ... 201
Find the sum of first n odd natural numbers
How many terms of the A.P. : 24, 21, 18, ................ must be taken so that their sum is 78?
If the numbers a, 9, b, 25 from an AP, find a and b.
How many three-digit natural numbers are divisible by 9?
What is the sum of first n terms of the AP a, 3a, 5a, ....
How many terms of the AP 63, 60, 57, 54, ... must be taken so that their sum is 693? Explain the double answer.
If the sum of three consecutive terms of an increasing A.P. is 51 and the product of the first and third of these terms is 273, then the third term is
How many terms of the A.P. 27, 24, 21, ..., should be taken so that their sum is zero?
Find the sum of three-digit natural numbers, which are divisible by 4.
Find t21, if S41 = 4510 in an A.P.
In an AP if a = 1, an = 20 and Sn = 399, then n is ______.
If the nth term of an AP is (2n + 1), then the sum of its first three terms is ______.
Find the sum of those integers from 1 to 500 which are multiples of 2 or 5.
[Hint (iii) : These numbers will be : multiples of 2 + multiples of 5 – multiples of 2 as well as of 5]
The sum of first five multiples of 3 is ______.
Find the sum of all the 11 terms of an A.P. whose middle most term is 30.
Read the following passage:
|
India is competitive manufacturing location due to the low cost of manpower and strong technical and engineering capabilities contributing to higher quality production runs. The production of TV sets in a factory increases uniformly by a fixed number every year. It produced 16000 sets in 6th year and 22600 in 9th year. |
- In which year, the production is 29,200 sets?
- Find the production in the 8th year.
OR
Find the production in first 3 years. - Find the difference of the production in 7th year and 4th year.
The sum of all two digit numbers is ______.
The nth term of an Arithmetic Progression is given by which expression?
