Question

If the Sum of first 6 terms of an A.P is 9 and the sum of its 9 terms is 6, then find the sum of its 15 terms?

Pls help me.....​

Answer 1

Sum of it's 15 terms is -15

Explanation:

S6=n/2{2a+(n-1)d}

9=6/2{2a+(6-1)d}

9=3{2a+(5)d}

9=3{2a+5d}

9=6a+15d

6=9/2{2a+(n-1)d}

6=4.5{2a+(9-1)d}

6=4.5{2a+(8)d}

6=4.5(2a+8d)

6=9a+36d

6a+15d=9 (1)

9a+36d=6 (2)

Multiply (1) by 6 and (2) by 4

36a+90d=54

36a+144d=24

Subtract (2) from (1)

-54d=30

d=30/-54

d=-10/18

=-5/9

9a+36d=6

9a+36(-5/9)=6

9a-180/9=6

9a-20=6

9a=6+20

9a=26

a=26/9

Check

6a+15d=9

6(26/9)+15(-5/9)

=156/9-75/9

=17.33-8.33

=9

Sum of it's 15 terms=n/2{2a+(n-1)d}

=15/2{2(26/9) + (15-1)-5/9}

=7.5{52/9 + (14)-5/9}

=7.5{52/9 -70/9}

=390/9-525/9

=390-525/9

=-135/9

=-15

Sum of it's 15 terms is -15