Question

Sum of fint nth term of an arithmetic sequence is 8nsquare +59 9) Find the sum of first 20 terms b)write the algebraic expression of the Sequence ​

Answer 1

Answer:

Given an arithmetic sequence with the first term a1a1 and the common difference dd , the nthnth (or general) term is given by an=a1+(n−1)dan=a1+(n−1)d .

Step-by-step explanation:

Find the 27th27th term of the arithmetic sequence  5,8,11,54,...5,8,11,54,... .

a1=5,  d=8−5=3a1=5,  d=8−5=3

So,

a27=5+(27−1)(3)        =83

Find the 40th40th term for the arithmetic sequence in which

a8=60a8=60 and a12=48a12=48 .

Substitute 6060 for a8a8 and 4848 for a12a12 in the formula

an=a1+(n−1)dan=a1+(n−1)d  to obtain a system of linear equations in terms of a1a1 and dd .

a8=a1+(8−1)d→60=a1+7da12=a1+(12−1)d→48=a1+11da8=a1+(8−1)d→60=a1+7da12=a1+(12−1)d→48=a1+11d

Subtract the second equation from the first equation and solve for dd .

12=−4d−3=d12=−4d−3=d

Then 60=a1+7(−3)60=a1+7(−3) .  Solve for aa .

60=a1−2181=a160=a1−2181=a1

Now use the formula to find a40a40 .

a40=81+39

Answer 2

Answer:

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