Question

the sum of first 5 terms of an arithmetic sequence is 100 and the sum of first 10 terms of an arithmetic sequence is 350
a.find 3rd term
b.find 8th term
c.find the sum of 5th term and 6th term
d.find the sum of 1st n terms​

Answer 1

Answer:

since, given that

S5= 100----------------1)

and S10=350------------2)

we know that

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

S5= 5/2{2a+(5-1) d}

100=5/2{2a+4d}

100/5=a+2d

20=a+2d----------3)

and

S10=10/2{2a+(9-1) d}

350=5{2a+8d}

350/5=2(a+4d)

70/2=a+4d

35=a+4d-----------4)

now,

eq. (4) - eq. (3)

2d =15

d=15/2

putting the value of d in (3)

a+2d=20

a+15=20

a= 20-15

a=5

therefore,

1::::: a3= a+2d=5+15=20

2::::: a8=a+7d=5+105/2=115/2

3::::::: a5+a6=a+4d+a+5d=2a+9d=10+135/2=155/2

4::::: Sn= n/2{2×5+(n-1) 15/2}

=n/2{10+15n/2-15/2}

=n/2(5/2+15n/2)

=n(5+15n)

=5n+15n^2