2 Views

Question : The sum of 10 terms of the arithmetic series is 390. If the third term of the series is 19, find the first term:

Option 1: 3

Option 2: 5

Option 3: 7

Option 4: 8


Team Careers360 8th Jan, 2024
Answer (1)
Team Careers360 16th Jan, 2024

Correct Answer: 3


Solution : Given: The sum of 10 terms of the arithmetic series is 390.
So, $n=10$
The third term of the series is 19.
Let the first term of the series be $a$.
We know, sum of arithmetic progression (A.P.) = $\frac{n}{2}[2a+(n-1)d]$
$n^{th}$ term = $a+(n-1)d$
So, $3^{rd}$ term ⇒ $a+(3-1)d=19$
⇒ $a+2d=19$ ----------------------------(1)
Sum of 10 terms = $\frac{10}{2}[2a+(10-1)d] =390$
⇒ $2a+9d=78$ ---------(2)
Multiplying 9 with equation (1) and 2 with equation (2), we get,
⇒ $9a+18d=171$ ------------------------(3)
⇒ $4a+18d=156$ ------------------------(4)
Subtracting (4) from (3), we get,
$5a=15$
$\therefore a=3$
Hence, the correct answer is 3.

SSC CGL Complete Guide

Candidates can download this ebook to know all about SSC CGL.

Download EBook

Know More About

Related Questions

TOEFL ® Registrations 2024
Apply
Accepted by more than 11,000 universities in over 150 countries worldwide
Manipal Online M.Com Admissions
Apply
Apply for Online M.Com from Manipal University
View All Application Forms

Download the Careers360 App on your Android phone

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

150M+ Students
30,000+ Colleges
500+ Exams
1500+ E-books