Question

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

Answer 1

$given,$

$in \: \: an \: \: ap,$

$first \: \: term ,\: \: a = - 5$

$d = 2$

$sum \: \: of \: \: first \: \: 6 \: \: terms =$

$\frac{n}{2} (2a + (n - 1)d)$

$n = 6$

$\frac{6}{2} (2 \times - 5 + (6 - 1)2)$

$3( - 10 + 10)$

$= 0$

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Answer 2

Given :

• Fisrt term ( a ) = - 5

• Common difference ( d ) = 2

• Number of term ( n ) = 6

To Find :

• Sum of first 6 terms

Solution :

By using A.P formula

$\large\implies\boxed{\sf \purple{S_n = \dfrac{n}{2} \bigg[2a + (n - 1)d \bigg]}}$

Substitute values in formula

$\implies \sf S_6 = \frac{6}{2} \bigg[2 \times ( - 5) + (6 - 1)2 \bigg]\\ \\\implies \sf S_6 =3[- 10 + 10 \: ] \\ \\\implies \sf S_6 =3 \times 0 \\ \\ \large \implies \boxed{\sf S_6 =0}$