LIVE Course for free

Rated by 1 million+ students
Get app now
0 votes
108 views
in Mathematics by (54.3k points)
closed by

The nth term of an A.P is \(\frac{{2\; + \;{\rm{n}}}}{3}\), then the sum of first 97 terms is


1. 1648
2. 1561
3. 1649
4. 1751
5. None of these

1 Answer

0 votes
by (30.0k points)
selected by
 
Best answer
Correct Answer - Option 3 : 1649

Concept:

Let us consider sequence a1, a2, a3 …. an is an A.P.

  • Common difference “d”= a2 – a1 = a3 – a2 = …. = an – an – 1
  • nth term of the A.P. is given by an = a + (n – 1) d
  • nth term from the last is given by an = l – (n – 1) d
  • sum of the first n terms = S = n/2[2a + (n − 1) × d] Or sum of the first n terms = n/2(a + l)


Where, a = First term, d = Common difference, n = number of terms and an = nth term

Calculation:

Given: nth term of an A.P = an\(\frac{{2\; +\; {\rm{n}}}}{3}\)

For first term, put n = 1

a1 = a = (2 + 1)/3 = 3/3 = 1

For last term, put n = 97

l = (97 + 2)/3 = 99/3 = 33

We have to find the sum of first 97 terms,

S = (97/2) (1 + 33)    (∵ S = n/2(a + l))

S = 97 × 17 = 1649

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...