Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • The first term of an AP is -5 and the last term is 45. If the sum of the terms of the AP is 120, then find the number of terms and the common difference.

The first term of an AP is -5 and the last term is 45. If the sum of the terms of the AP is 120, then find the number of terms and the common difference.

Answers (1)

\\$Given that a $= - 5, a\textsubscript{n} = 45, S\textsubscript{n} = 120\\ a\textsubscript{n}= 45\\ a + (n - 1) \times d = 45 (using a\textsubscript{n} = a + (n-1).d)\\ -5 + (n-1) \times d = 45\\ (n - 1) \times d = 50 $ \ldots $ (1)\\ S\textsubscript{n} = 120\\ {{S}_{n}}=\frac{n}{2}\left[ 2a+\left( n-1 \right)d \right] = 120\\ \frac{n}{2}\left[ -10+50 \right]=120 Using (1)\\ n \times (40) = 240\\ n = 24/4 = 6\\ $ Number of terms (n)$= 6\\ Put n = 6 in (1)\\ (6 - 1) \times d = 50\\ 5d = 50\\ d = 10\\ $Common difference $= 10\\

Posted by

infoexpert21

View full answer

Similar Questions

Latest Question