Advertisements
Advertisements
Question
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)
Solution
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
RELATED QUESTIONS
If the ratio of the sum of first n terms of two A.P’s is (7n +1): (4n + 27), find the ratio of their mth terms.
Find the sum of first 30 terms of an A.P. whose second term is 2 and seventh term is 22
Find the sum given below:
–5 + (–8) + (–11) + ... + (–230)
Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.
Find the sum of first 40 positive integers divisible by 6.
Find the sum to n term of the A.P. 5, 2, −1, −4, −7, ...,
In an A.P., if the 5th and 12th terms are 30 and 65 respectively, what is the sum of first 20 terms?
The sum of n natural numbers is 5n2 + 4n. Find its 8th term.
How many two-digit number are divisible by 6?
Show that `(a-b)^2 , (a^2 + b^2 ) and ( a^2+ b^2) ` are in AP.
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 a certain number of terms starting from first term of an A.P. is 25, 22, 19, ..., is 116. Find the last term.
The sum of the first n terms of an A.P. is 3n2 + 6n. Find the nth term of this A.P.
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 nth term of the \[A . P . \frac{1}{m}, \frac{1 + m}{m}, \frac{1 + 2m}{m}, . . . .\]
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 sum of the first three terms of an Arithmetic Progression (A.P.) is 42 and the product of the first and third term is 52. Find the first term and the common difference.
Find the sum of all members from 50 to 250 which divisible by 6 and find t13.
If the third term of an A.P. is 1 and 6th term is – 11, find the sum of its first 32 terms.
Find the sum of those integers between 1 and 500 which are multiples of 2 as well as of 5.
