Six numbers are in an AP such that their sum | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let the six terms of the $AP$ be $a-5d, a-3d, a-d, a+d, a+3d, a+5d$ with common difference $2d$. Sum of the terms $= (a-5d) + (a-3d) + (a-d) + (a+

Vedclass · Accepted Answer

-$4$

Vedclass · Answer

(D) Let the six terms of the $AP$ be $a-5d, a-3d, a-d, a+d, a+3d, a+5d$ with common difference $2d$. Sum of the terms $= (a-5d) + (a-3d) + (a-d) + (a+d) + (a+3d) + (a+5d) = 6a$. Given $6a = 3$, so $a = \frac{1}{2}$. Given $T_1 = 4T_3$, where $T_1 = a-5d$ and $T_3 = a-d$. $a-5d = 4(a-d)$ $\Rightarrow a-5d = 4a-4d$ $\Rightarrow -3a = d$. Substituting $a = \frac{1}{2}$, we get $d = -3 	imes \frac{1}{2} = -\frac{3}{2}$. The fifth term is $T_5 = a+3d$. $T_5 = \frac{1}{2} + 3(-\frac{3}{2}) = \frac{1}{2} - \frac{9}{2} = -\frac{8}{2} = -4$.

Six numbers are in an $AP$ such that their sum is $3$. The first term is $4$ times the third term. Then, the fifth term is:

Similar Questions

The sum of the common terms of the following three arithmetic progressions:
$3, 7, 11, 15, \ldots, 399$
$2, 5, 8, 11, \ldots, 359$ and
$2, 7, 12, 17, \ldots, 197$,is equal to $................$.

If $a + 2b + 3c = 6$,then the greatest value of $abc^2$ is (where $a, b, c$ are positive real numbers).

If the arithmetic mean between the $p^{th}$ term and $q^{th}$ term of an arithmetic progression is equal to the arithmetic mean between its $r^{th}$ and $s^{th}$ term,then $p + q = ......$

If the middle term of the $AP$ is $300$,then the sum of its first $51$ terms is

The arithmetic mean of the first $n$ even natural numbers is ..........

Vedclass Test Series

Exam Paper Generator

Online Exam Module