The 16th term of an A.P. is 40 and the sum of the first 5 terms is 5. Find the sum of the first 50 terms.
in Algebra 2 Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

2 Answers

This should help:

by Level 10 User (57.4k points)

An AP has the form, a, a+d, a+2d, ...

The general term is a+(n-1)d.

If n=16 the 16th term is a+15d=40.

The sum of the first 5 terms is 5a+d(0+1+2+3+4)=5a+10d=5, so a+2d=1, therefore a=1-2d.

(0+1+2+3+4)=5*4/2=10=n(n-1)/2 where n=5.

Substitute for a:

1-2d+15d=40, 13d=39 so d=3 and a=1-2d=1-6=-5.

The AP is: -5, -2, 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, ...

Sum of the first 50 terms is 50(-5)+3(0+1+2+3+...+49)=-250+3(50)(49)/2=3425.

by Top Rated User (1.2m points)

Related questions

1 answer
1 answer
asked Jun 20, 2013 in Algebra 2 Answers by anonymous | 815 views
1 answer
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
87,516 questions
100,289 answers
2,420 comments
738,303 users