Question

if the nth term of an AP is 9-5n . Find the sum of first 10terms.

Answer 1

Given that the nth term of the AP is 9 - 5n


First, assume the value of n in the nth term. Assume nth term = 1st term. According to the question, nth term = 9 - 5n. Similarly :


1st term = 9 - 5( 1 )

1st term = 9 - 5

1st term = 4


Now again assuming the value of n in nth term. Assuming nth term = 10th term. Similarly :

10th term = 9 - 5( 10 )

10th term = 9 - 50

10th term = - 41



$Applying \: \: the \: \: formula \: \: s_{n} = \dfrac{n}{2} (a + l )$

Where, l is the last or 10th term in the question and a is the 1st term


So,


$S_{10} = \dfrac{ 10}{2}[ 4 + ( - 41 ) ] \\ \\ \\ S_{10}= 5[ 4 - 41 ] \\ \\ S_{10}= 5( - 37) \\ \\ \\ S_{10}= -185$



Therefore, Sum of 10 terms of the AP is - 185.