Question

if the sum of one term is 2 and the sum of the two-term is 0 the sum of 100 terms is?

Answer 1

Answer:

$\bigstar\:\:\:\huge\boxed{S_{100}=\:-9700}\:\:\:\bigstar$

Explanation :

✦ Given :–

• S₁=2 (Sum of first one term)
• S₂=0 (Sum of first two terms)

✦ To Find :–

• S₁₀₀ (Sum of First 100 Terms)

✦ Formula Applied :–

• Sₙ=$\frac{n}{2}$[2a+(n-1)d]

• aₙ=a+(n-1)d

✦ Solution :–

→ S₁=a

∴ a=2

→ S₂=a₁+a₂

∴ 0=2+a₂

⇒ a₂=(-2)

→ d=a₂-a₁=0-2=(-2)

∴ d=(-2)

Now we need to find S₁₀₀ :

$\implies S_{100}=\frac{100}{2} [2(2)+(100-1)(-2)]$

$\implies S_{100}=50\times [4+(99)(-2)]$

$\implies S_{100}=50\times [4-198]$

$\implies S_{100}=50\times(-194)$

$\implies \boxed{S_{100}=(-9700)}$

∴ The Sum of first 100 terms is (-9700).

Answer 2

Step-by-step explanation:

Answer:

\bigstar\:\:\:\huge\boxed{S_{100}=\:-9700}\:\:\:\bigstar★

S

100

=−9700

★

Explanation :

✦ Given :–

S₁=2 (Sum of first one term)

S₂=0 (Sum of first two terms)

✦ To Find :–

S₁₀₀ (Sum of First 100 Terms)

✦ Formula Applied :–

Sₙ=\frac{n}{2}

2

n

[2a+(n-1)d]

aₙ=a+(n-1)d

✦ Solution :–

→ S₁=a

∴ a=2

→ S₂=a₁+a₂

∴ 0=2+a₂

⇒ a₂=(-2)

→ d=a₂-a₁=0-2=(-2)

∴ d=(-2)

Now we need to find S₁₀₀ :

\implies S_{100}=\frac{100}{2} [2(2)+(100-1)(-2)]⟹S

100

=

2

100

[2(2)+(100−1)(−2)]

\implies S_{100}=50\times [4+(99)(-2)]⟹S

100

=50×[4+(99)(−2)]

\implies S_{100}=50\times [4-198]⟹S

100

=50×[4−198]

\implies S_{100}=50\times(-194)⟹S

100

=50×(−194)

\implies \boxed{S_{100}=(-9700)}⟹

S

100

=(−9700)

∴ The Sum of first 100 terms is (-9700).