Question

Dhe sum of an A. P. is 40, its common difference is 2 and its last
term is 13, find its first term and the number of terms.
[Ans. : a = = 7, n = 4 or a = -5, n = 10]​

Answer 1

Answer:

an=13

a+(n-1)d=13

a+(n-1)2=13

a+2n-2=13

a+2n=15

a=15-2n.. (1)

Sn=n/2(a+l)

40=n/2(15-2n+13)

80/n=28-2n

28n-2n²=80

2n²-28n+80=0

n²-14n+40=0

n²-10n-4n+40=0

n(n-10)-4(n-10)=0

(n-10)(n-4)=0

n-10=0,n-4=0

n=10,n=4

putting and equal 4 in equation first

a=15-2×4=7

putting n equal 10 in equation first

a=15-2×10= -5