(D) Given that,$a_{12}=37$ and $d=3$.Using the formula for the $n^{th}$ term of an $AP$,$a_n = a + (n-1)d$.For $n=12$,$a_{12} = a + (12-1)3$.$37 = a +

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

(D) Given that,$a_{12}=37$ and $d=3$.Using the formula for the $n^{th}$ term of an $AP$,$a_n = a + (n-1)d$.For $n=12$,$a_{12} = a + (12-1)3$.$37 = a + 11(3)$.$37 = a + 33$.$a = 37 - 33 = 4$.Now,to find the sum of the first $12$ terms,we use the formula $S_n = \frac{n}{2}[a + a_n]$.$S_{12} = \frac{12}{2}[4 + 37]$.$S_{12} = 6(41)$.$S_{12} = 246$.

Class 10 Mathematics Arithmetic Progressions Textbook -Arithmetic Progressions

Medium

In an $AP$ given $a_{12}=37$ and $d=3$,find the first term $a$ and the sum of the first $12$ terms $S_{12}$.

A
$254$
B
$259$
C
$240$
D
$246$

Explore More

Browse All

Question Bank

All Subjects

Class 10 Questions

Class 10

Mathematics Questions

Chapter

Arithmetic Progressions

Subtopic

Textbook -Arithmetic Progressions

Which term of the $AP: 21, 18, 15, \ldots$ is $-81$? Also,is any term $0$? Give reason for your answer.

Medium

View Solution

Do $4, 10, 16, 22, \ldots$ form an $AP$? If they form an $AP,$ write the next two terms.

Easy

View Solution

In an $AP$,given $a_{3} = 15$ and $S_{10} = 125$,find $d$ and $a_{10}$.

Medium

View Solution

Are $a, a^{2}, a^{3}, a^{4}, \ldots$ in an $AP$? If they form an $AP$,find the common difference $d$ and write three more terms.

Medium

View Solution

In an $AP$,given $l = 28$,$S = 144$,and there are a total of $9$ terms. Find $a$.

Easy

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

In an $AP$ given $a_{12}=37$ and $d=3$,find the first term $a$ and the sum of the first $12$ terms $S_{12}$.

Similar Questions

Which term of the $AP: 21, 18, 15, \ldots$ is $-81$? Also,is any term $0$? Give reason for your answer.

Do $4, 10, 16, 22, \ldots$ form an $AP$? If they form an $AP,$ write the next two terms.

In an $AP$,given $a_{3} = 15$ and $S_{10} = 125$,find $d$ and $a_{10}$.

Are $a, a^{2}, a^{3}, a^{4}, \ldots$ in an $AP$? If they form an $AP$,find the common difference $d$ and write three more terms.

In an $AP$,given $l = 28$,$S = 144$,and there are a total of $9$ terms. Find $a$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module