Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • In an A.P., the first term is 2 and the sum of the first five terms is one-fourth of the next five terms. Show that 20 th term is minus 112.

3.  In an A.P., the first term is 2 and the sum of the first five terms is one-fourth of the next five terms. Show that 20th term is –112. 

Answers (1)

best_answer

First term =a=2

Let the series be 2,2+d,2+2d,2+3d,.......................

Sum of first five terms =10+10d

Sum of next five terms =10+35d

Given : The sum of the first five terms is one-fourth of  the next five terms.

10+10d=\frac{1}{4}(10+35d)

\Rightarrow \, \, 40+40d=10+35d

\Rightarrow \, \, 40-10=35d-40d

\Rightarrow \, \, 30=-5d

\Rightarrow \, \, d=-6

To prove  : a_2_0=-112

L.H.S : a_2_0=a+(20-1)d=2+(19)(-6)=2-114=-112=R.H.S

Hence, 20th term is –112.

 

Posted by

seema garhwal

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Class 12 board exams 2025 to have 50% competency-based questions; no change in 10th
anam-khan

CBSE Class 12 board exams 2024 over; expected result date, trends of last 10 years

Latest Question