Question

for an AP, a= -10, d=4. find S¹0

Answer 1

Answer :

$\large\boxed{ \star \: \: \bf{s_{10} \: = \: 80 \: \:\star }}$

Explanation :

Given :–

• a = (-10)
• d = 4

To Find :–

• $s_{10} \: (sum \: of \: first \: 10 \: terms)$

Formula Applied :–

• $\boxed{ \star \: \: \bf{s_n \: = \: \dfrac{n}{2}[2a \: + \: (n \: - \: 1)d] } \: \: \star }$

Solution :–

We have ,

• a = (-10)
• d = 4
• n = 10

Putting these values in the Formula :

$\rightarrow\sf{s_n \: = \: \dfrac{n}{2}[2a \: + \: (n \: - \: 1)d]}$

$\rightarrow\sf{s_{10} \: = \: \dfrac{10}{2}[2( - 10) \: + \: (10\: - \: 1)(4)]}$

$\rightarrow\sf{s_{10} \: = \: 5[( - 20) \: + \: (9 \: \times \: 4)]}$

$\rightarrow\sf{s_{10} \: = \: 5[( - 20) \: + \: 36]}$

$\rightarrow\sf{s_{10} \: = \: 5 \: \times \:16 }$

$\rightarrow \boxed{\bf{s_{10} \: = \: 80 }}$

∴ The Sum of 10 Terms will be 80 .

Answer 2

◘ Given ◘

In an AP,

• a = -10
• d = 4

◘ To Find ◘

The value of S₁₀ (The sum of first 10 terms of the given AP).

◘ Solution ◘

We know,

$\boxed{\rm{S_n=\frac{n}{2}[2a+(n-1)d]}}$

Now, using the above formula :-

$\rm{\longrightarrow S_{10}= \dfrac{10}{2}[2(-10)+(10-1)4] }\\\\\rm{\longrightarrow S_{10}= 5[-20+4(9)]}\\\\\rm{\longrightarrow S_{10}= 5(-20+36)}\\\\\rm{\longrightarrow S_{10}= 5\times16}\\\\\huge\underline{\overline{\mid{\bold{ \orange{S_{10}=80}}\mid}}}$

Therefore, the sum of first 10 terms is 80.