Question

Which expression defines the given series for seven terms? –3 + (–1) + 1 + . . .

a.Σ (2n-5)
b.Σ (2-5n) c.Σ (5n-2) d.Σ (5-2n)

Answer 1

`-3+(-1)+1+...\\\\a_1=-3;\ a_2=-1;\ a_3=1\\\\It's\ an\ arithmetic\ sequence\ where\ the\ common\ difference\\is\ equal\ d=a_2-a_1=-1-(-3)=-1+3=2.\\\\a_n=a_1+(n-1)d\\\\a_n=-3+(n-1)\cdot2=-3+2n-2=2n-5\\\\Answer:\boxed{\sum\limits_(n=1)^7(2n-5)}\to\fbox{a.}`

Answer 2

Answer:
`\sum^(7)_(n=1)(2n-5)`

Explanation:

Given: The first term of the series
`a= -3`

The second term of the series
`a_2= -1`

The third term of the series
`a_3= 1`

The common difference=
`d=a_3-_a_2=a_2-a_1=2`

Now, the nth term of this series will be given by :-

`a_n=a+d(n-1)\\\\\Rightarrow\ a_n=-3+2(n-1)\\\\\Rightarrow\ a_n=-3+2n-2\\\\\Rightarrow\ a_n=2n-5`

Hence, the expression defines the given series for seven terms will be

`\sum^(7)_(n=1)(2n-5)`