Question
Download Solution PDFThe sum of the 3rd and the 7th term of an A.P. is 30 and the sum of the 5th and the 9th term is 56. Find the sum of the 4th and the 8th terms of the same series.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
The nth number in A.P. series (an) = a + (n-1)d
The sum of the n numbers in the series = \(\rm {n\over2}\left[2a + (n-1)d\right]\)
Where 'a' is the first number of the series and 'd' is the common difference
Calculation:
Let the first term of the A.P. be 'a' and the common difference be 'd'
Given a3 + a7 = 30
a + 2d + a + 6d = 30
2a + 8d = 30 ...(i)
Also given a5 + a9 = 56
a + 4d + a + 8d = 56
2a + 12d = 56 ...(ii)
Adding (i) and (ii)
4a + 20d = 86
2a + 10d = 43
a + 3d + a + 7d = 43
a4 + a8 = 43
Last updated on May 30, 2025
->UPSC has released UPSC NDA 2 Notification on 28th May 2025 announcing the NDA 2 vacancies.
-> A total of 406 vacancies have been announced for NDA 2 Exam 2025.
->The NDA exam date 2025 has been announced for cycle 2. The written examination will be held on 14th September 2025.
-> Earlier, the UPSC NDA 1 Exam Result has been released on the official website.
-> The selection process for the NDA exam includes a Written Exam and SSB Interview.
-> Candidates who get successful selection under UPSC NDA will get a salary range between Rs. 15,600 to Rs. 39,100.
-> Candidates must go through the NDA previous year question paper. Attempting the NDA mock test is also essential.