For an A.P.,the 5^{th} term is 30 and the 12^ | vedclass

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

Question

(B) Let the first term be $a$ and the common difference be $d$.The $n^{th}$ term of an $A.P.$ is given by $a_n = a + (n - 1)d$.For the $5^{th}$ term:

Vedclass · Accepted Answer

$1700$

Vedclass · Answer

(B) Let the first term be $a$ and the common difference be $d$.The $n^{th}$ term of an $A.P.$ is given by $a_n = a + (n - 1)d$.For the $5^{th}$ term: $a + 4d = 30$  --- $(1)$For the $12^{th}$ term: $a + 11d = 100$ --- $(2)$Subtracting equation $(1)$ from $(2)$:$(a + 11d) - (a + 4d) = 100 - 30$$7d = 70$$d = 10$Substituting $d = 10$ in equation $(1)$:$a + 4(10) = 30$$a + 40 = 30$$a = -10$The sum of the first $n$ terms is $S_n = \frac{n}{2} [2a + (n - 1)d]$.For $n = 20$:$S_{20} = \frac{20}{2} [2(-10) + (20 - 1)10]$$S_{20} = 10 [-20 + 190]$$S_{20} = 10 [170]$$S_{20} = 1700$.

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 an $A.P.$,the $5^{th}$ term is $30$ and the $12^{th}$ term is $100$. Find the sum of the first $20$ terms of the $A.P.$

Similar Questions

If the sum of the first $6$ terms of an $AP$ is $36$ and that of the first $16$ terms is $256,$ find the sum of the first $10$ terms.

If $x+1, 3x$ and $4x+2$ are three consecutive terms of an $A.P.$,find the value of $x$.

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: $111, 107, 103, 99, \ldots$

The sequence $1, 3, 6, 10, \ldots$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module