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nata0808 [166]
2 years ago
7

2. The sum of two numbers is 67. The

Mathematics
1 answer:
DaniilM [7]2 years ago
5 0

Answer:

below

Step-by-step explanation:

l = large no

s = small no

l=s+13

l+s = 67

s+13+s = 67

2s+13 = 67

2s = 54

s=27

l= 40

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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]
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