Question

. How many terms are there in the A.P. whose first and sixth terms are −13 and 12 respectively and sum of all these terms is 132 ?

Answer 1

Answer:

we know that

nth term= a+(n-1)d

6 term = -12+(6-1)d

8=-12+(5)d

20=5d

4=d. (1)

we know that

s nth =1/2 × n × (1st term + last term)

120=n/2 (2 (-12)+(n-1)d)

120=n/2 (-24+4n-4)

120=n (-12+2n-2)

120=-12n+2n^2-2n

120=2n^2-14n

60=n^2-7n

n^2-7n-60=0

n^2-12n+5n-60=0

n (n-12)+5 (n-12)

n+5 and n-12

n=-5 and 12

terms cannot be negative

therefore terms are 12