Question

If the first term of an AP is -5 and the common difference is 2, then the sum of the first 6 terms is

Answer 1

Given :-

• first term, a = -5
• common difference = 2

To Find :-

• find the sum of first 6 terms of AP ?

Solution :-

we know that,

$\boxed{ \pink{\bold{S _{n} = \frac{n}{2} \{2a + (n - 1)d \}}}}$and here,

• n = 6
• a = -5
• d = 6

$\bold{: \implies S _{6} = \cancel \frac{6}{2} \{2 \times - 5 + (6 - 1)2 \}} \\ \\ \bold{: \implies S _{6} = 3( - 10 + 5 \times 2)} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies S _{6} = 3( - 10 + 10) } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies \: S _{6} = 3 \times 0} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies \boxed{ \bold{S _{6} = 0}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

hence, sum of first 6 terms of AP is 0