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Taking first summation ∑(1+3n) first

First see few terms of this series. To get first term plug n =0 in 1+3n

So for n =0,

similarly for next term plug n =1

For n = 1,

For n =2,

So on ,........and last term will be for n =4

For n =4,

So we get terms as 1,4,7,.. with constant difference of 3 between succesive terms. So its arithemetic series. Sum formula for arithmetic series is

where n is total number of terms, and are first and last term in series

So here n = 5 ( as n is from 0 till 4). so plug value of n as 5, as 1 and as 13 in sum formula

So sum of first series is 35

Similarly find sum of second series. Plug i values in 3i-5 as shown and find few terms in series

for i =2,

for i =3,

so on .... and for last term plug i as 6

for i =6,

So for sum we will plug n as 5 ( i =2,3,4,5,6 so total 5 terms), then plug as -2 and as 13 in sum formula

So sum of second series is also 35

So difference between sums of both series will be 35-35 =0

Final answer here is 0

48 qt = 12 gallons

Hint : 1 quarts = 0.25

if 1 quarts = 0.25 gallon

    48 quarts = x gallons

1x = 48*0.25

1x = 12 gallons

x = 12/1

x= 12 gallons

I hope that's help ! easy right ... Good night dude

A. Prove that QR ≅ QR by reflexive property

Nikki is going to use SSS Property, which is Side, Side, Side. This means that, given two pairs of sides are congruent, you will have to find out the last side, which is the same side. This means that it is congruent with itself (since both triangles share the same side), and uses the reflexive property.

hope this helps

Answer: A is the correct answer

Step-by-step explanation: