For a given A.P.,the 5^{th} term is 30 and th | vedclass

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

Question

(D) Let the first term be $a$ and the common difference be $d$.The $n^{th}$ term of an $A.P.$ is given by $a_n = a + (n-1)d$.Given $a_5 = 30$,so $a +

Vedclass · Accepted Answer

$2475$

Vedclass · Answer

(D) Let the first term be $a$ and the common difference be $d$.The $n^{th}$ term of an $A.P.$ is given by $a_n = a + (n-1)d$.Given $a_5 = 30$,so $a + 4d = 30$ (Equation $1$).Given $a_{12} = 65$,so $a + 11d = 65$ (Equation $2$).Subtracting Equation $1$ from Equation $2$: $(a + 11d) - (a + 4d) = 65 - 30$.$7d = 35$,which gives $d = 5$.Substituting $d = 5$ into Equation $1$: $a + 4(5) = 30 \implies a + 20 = 30 \implies a = 10$.The sum of the first $n$ terms is $S_n = \frac{n}{2} [2a + (n-1)d]$.For $n = 30$: $S_{30} = \frac{30}{2} [2(10) + (30-1)5]$.$S_{30} = 15 [20 + 29 	imes 5] = 15 [20 + 145] = 15 	imes 165 = 2475$.

Part $I$	Part $II$
$1$. Sixth term of the $A.P.$ $1, 3, 5, 7, \ldots$	$a$. $105$
$2$. Eleventh term of the $A.P.$ $3, 6, 9, 12, \ldots$	$b$. $11$
$3$. Sixteenth term of the $A.P.$ $4, 6, 8, 10, \ldots$	$c$. $33$
$4$. Twenty-first term of the $A.P.$ $5, 10, 15, 20, \ldots$	$d$. $34$

For a given $A.P.$,the $5^{th}$ term is $30$ and the $12^{th}$ term is $65$. Find the sum of first $30$ terms of this $A.P.$

Similar Questions

Which term of the $A.P.$ $85, 78, 71, \ldots$ is its first negative term? If the order of this term is $n$,find $S_{n}$.

Which term of the $A.P.$ $83, 77, 71, \ldots$ is its first negative term (in $^{th}$)?

For the $A.P.$ formed by positive multiples of $4$,$d = \ldots \ldots \ldots \ldots .$

Determine whether the following sequence is an $A.P.$ or not. (Assume that the pattern continues.) If it is an $A.P.$,find its $n^{th}$ term: $111, 107, 103, 99, \ldots$

Vedclass Test Series

Exam Paper Generator

Online Exam Module