Answer:
Explanation:
This is the formula to find the sum of the first
n
terms of the sequence. To evaluate it, the values of the first and
n
the terms must be found .Sn=n2⋅(a1+an)
This is an arithmetic sequence since there is a common difference between each term. In this case, adding
6
to the previous term in the sequence gives the next term. In other words,
an=a1+d(n−1)x Arithmetic Sequence:
d=6 This is the formula of an arithmetic sequence X an=a1+d(n−1)Substitute in the values of a1=4 and d=6 x an=4+(6)(n−1)Simplify each term.
an=4+6n−6 Subtract 6 from 4 x an=6n−2 Substitute in the value of N to find the N the term x a5=6(5)−2 Multiply 6 by 5 x a5=30−2 Subtract 2 from 30 x a5=28 Replace the variables with the known values to find
S5 x S5=52⋅(4+28)Add 4 and 28 x S5=52⋅32
Cancel the common factor of
2.
S5=5⋅16 Multiply 5 by 16 x S5=80
Convert the fraction to a decimal.
S5=80