Question

The last term of a series in AP is 40 and the sum of the series is 952.the common difference is -2.find the first term and the numbers of terms in the series

Answer 1

Ans:; a= 72 and n= 17

Explanation:

an= 40 ; Sn= 952; d= -2

an= a+(n-1)d =. 40= a+(n-1)-2

40= a-2n+2.

40-2=a-2n

38+2n= a------» 1.

Sn= n/2(2a+(n-1)d

952= n/2(2 (38+ 2n) +(n-1)-2)

1904= n(76+4n-2n+2)

1904= n(78+2n)

2n²+78n-1904=0

2(n²+39n-952)=0

n²+56n-17n-952=0

n(n+56)-17(n+56)=0

n-17= 0. and n+56=0

therefore:;... n= 17 ,✓✓

therefore; a= 38+2n as 1st

a= 38+2(17). = 38+34

=72//