In an arithmetic progression, the sum of the 3rd, 4th and 5th terms is 12. What is the sum of the first 7 terms?

This question was previously asked in
AAI Junior Assistant (Fire Service) Official Paper (Held On: 15 Nov, 2022 Shift 2)
View all AAI Junior Assistant Papers >
  1. 32
  2. 24
  3. 26
  4. 28

Answer (Detailed Solution Below)

Option 4 : 28
Free
ST 1: English
2.3 K Users
20 Questions 20 Marks 25 Mins

Detailed Solution

Download Solution PDF

Given:

Arithmetic progression (AP)

Sum of 3rd, 4th, and 5th terms = 12

Formula used:

nth term of an AP: an = a + (n - 1)d

Sum of first n terms of an AP: Sn = (n/2)[2a + (n - 1)d]

Where a is the first term and d is the common difference.

Calculation:

The 3rd, 4th, and 5th terms:

a3 = a + 2d

a4 = a + 3d

a5 = a + 4d

Sum of 3rd, 4th, and 5th terms = 12:

(a + 2d) + (a + 3d) + (a + 4d) = 12

3a + 9d = 12

a + 3d = 4 ... (1)

The sum of the first 7 terms (S7):

S7 = (7/2)[2a + (7 - 1)d]

S7 = (7/2)[2a + 6d]

S7 = 7(a + 3d)

Substitute a + 3d = 4 from equation (1):

S7 = 7 × 4

S7 = 28

∴ The sum of the first 7 terms is 28.

Latest AAI Junior Assistant Updates

Last updated on Apr 24, 2025

-> The AAI Junior Assistant Response Sheet 2025 has been out on the official portal for the written examination.

-> AAI has released 168 vacancies for Western Region. Candidates had applied online from 25th February to 24th March 2025.

-> A total number of 152 Vacancies have been announced for the post of Junior Assistant (Fire Service) for Northern Region.

-> Eligible candidates can apply from 4th February 2025 to 5th March 2025. 

-> Candidates who have completed 10th with Diploma or 12th Standard are eligible for this post.

-> The selection process includes a Computer Based Test, Document Verification, Medical Examination (Physical Measurement Test), Driving Test and a Physical Endurance Test.

-> Prepare for the exam with AAI Junior Assistant Previous year papers.

Get Free Access Now
Hot Links: teen patti bodhi teen patti win teen patti jodi teen patti master download teen patti game online