Answer:
Step-by-step explanation:
Looking at the given graph, the slope of the line is expressed as
Slope = (y2 - y1)/(x2 - x1)
y2 = 19.5
y1 = 9.5
x2 = 6
x1 = 1
Slope = (19.5 - 9.5)/(6-1)
Slope = 10/5 = 2
The successive terms is increasing by 2
The formula for the nth term of an arithmetic sequence is expressed as
Tn = a + (n - 1)d
Where
a is the first term of the sequence
n is the number of terms in the sequence.
d is the common difference.
From the information given,
a = 9.5
Tn = an
d = 2
The explicit rule for the arithmetic sequence will be
an = 9.5 + 2(n-1)
Answer:
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Step-by-step explanation:
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The answer can be 6/1 or just 6. And visit www.caculatorsoup.com
41-28=13 questions, but you also have to do 41 and 28, so 15 questions
First term ,a=4 , common difference =4-7=-3, n =50
sum of first 50terms= (50/2)[2×4+(50-1)(-3)]
=25×[8+49]×-3
=25×57×-3
=25× -171
= -42925
derivation of the formula for the sum of n terms
Progression, S
S=a1+a2+a3+a4+...+an
S=a1+(a1+d)+(a1+2d)+(a1+3d)+...+[a1+(n−1)d] → Equation (1)
S=an+an−1+an−2+an−3+...+a1
S=an+(an−d)+(an−2d)+(an−3d)+...+[an−(n−1)d] → Equation (2)
Add Equations (1) and (2)
2S=(a1+an)+(a1+an)+(a1+an)+(a1+an)+...+(a1+an)
2S=n(a1+an)
S=n/2(a1+an)
Substitute an = a1 + (n - 1)d to the above equation, we have
S=n/2{a1+[a1+(n−1)d]}
S=n/2[2a1+(n−1)d]
