In arithmetic sequence the su m of First t nine terms is 279 and the sum of the first twentyterms is 1280. Then (a) what is the 5th term of the sequence? by what is the 16th term of the sequence? (c) write the sequence? (d) find sum of first 'n' terms?. please answer the question d?
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S9=(9/2){2a1+(9-1)d=(9/2)(2a1+8d)=279
a1+4d=31 equation 1
S20=(20/2){2a1+19d)=1280
2a1+19d=128 equation 2
From equation 1 you get
a1=31-4d
put this value of a1 in equation 2
2(31-4d)+19d=128
62-8d+19d=128
11d=128-62=66
d=6
a1=31-24=7
a5=7+4×6=31
Sn=(n/2)(14+(n-1)6}
=n(14+6n-6)/2
=n(4+3n)=3n^2+4n Ans
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