in an AP 5th term is 12 and sum of 11term is 83 1/2 find 1st term and common difference
Answers
Answer:
First term of the AP is 326 / 11 and common difference is - 97 / 22
Step-by-step explanation:
It is given that the 5th term of the AP is 12 and sum of 11 terms is 83 1 / 2 or 167 / 2.
Let first term of the AP be a and common difference of
= > 5th term = 12
= > a + ( 5 - 1 )d = 12
= > a + 4d = 12
= > a = 12 - 4d ...( i )
= > Sum of 11 terms = 167 / 2
= > ( 11 / 2 )[ 2a + ( 11 - 1 )d ] = 167 / 2
= > 11 [ 2a + 10d ] = 167
Substituting the value of a from ( i ) :
= > 11[ 2( 12 - 4d ) + 10d ] = 167
= > 11[ 24 - 8d + 10d ] = 167
= > 24 + 2d = 167 / 11
= > 2d = 167 / 11 - 24
= > 2d = - 97 / 11
= > d = - 97 / 22
Therefore,
= > a = 12 - 4( - 97 / 22 )
= > a = 12 + 194 / 11
= > a = 326 / 11
Hence,
First term of the AP is 326 / 11 and common difference is - 97 / 22