How many terms are there in an AP .whose first terma and 6th term are -12 and 8 respectively.and sum of all in terms is 120
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hi all
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
hope this helps
mark as brainliest
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
hope this helps
mark as brainliest
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