Question

The sum of 4th and 6th terms in an arithmetic sequence is 20 A)find the sum of its 1st and 9th terms

Answer 1

t4=a+(n-1)d

=a+(4-1)d

=a+3d

t6=a+(n-1)d

=a+(6-1)d

=a+5d

We have given that their sum is 20

(a+3d)+(a+5d)=20

2a+8d=20 (1)

now we have to find sum of 1st and 9 th term

t1=a+(n-1)d

=a+(1-1)d

=a

t9=a+(n-1)d

=a+(9-1)d

=a+8d

sum of these two numbers

=a+a+8d

=2a+8d (2)

Now equation 1 and 2 are equal so their value must be equal

so sum of 1st and 9th term is 20