Question

If the first term of an ap is -5 and the cd is 2 , then the sum of the first 6 terms is

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Sum\:of\:first\:6\:terms=0}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies First \: term( a_{1})= - 5 \\ \\ \tt: \implies Common \: difference(d) = 2 \\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: \implies Sum \: of \: first \: 6 \: terms( s_{6}) =?$

• According to given question :

$\tt \circ \: a_{1} = - 5 \\ \\ \tt \circ \: d = 2\\ \\ \tt \circ \: n = 6 \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies s_{6} = \frac{n}{2} (2a + (n - 1)d) \\ \\ \tt: \implies s_{6} = \frac{6}{2} (2 \times ( - 5) + (6 - 1) \times 2 )\\ \\ \tt: \implies s_{6} = 3 \times ( - 10 + 5 \times 2) \\ \\ \tt: \implies s_{6} =3 \times( - 10 + 10) \\ \\ \tt: \implies s_{6} =3 \times 0 \\ \\ \green{\tt: \implies s_{6} = 0} \\ \\ \green{\tt \therefore Sum \: of \: first \: 6 \: terms \: of \:is \: 0}$

Answer 2

Aɴꜱᴡᴇʀ

☞ $\large \orange{ \tt{}s_6 = 0}$

_________________

Gɪᴠᴇɴ

➠ First term (a) = -5

➠ Their common difference (d) = 2

➠ The nth term = 6

_________________

ᴛᴏ ꜰɪɴᴅ

➜ The sum of the first 5 terms of the Arithmetic Progression

_________________

Sᴛᴇᴘꜱ

✭ So the sum of n terms is given by

$\tt \leadsto{}s_n = \frac{n}{2}(2a +(n - 1)d)$

Where,

➜ n = The nth term of the AP

➜ a = The first term of the AP

➜ d = Common difference

So substituting the given values,

$\tt \dashrightarrow{}s_6 = \frac{6}{2} (2( - 5) + (6 - 1)2) \\ \\ \tt \dashrightarrow{}s_6 = \cancel\frac{6}{2} ( - 10 + 10) \\ \\ \tt \dashrightarrow{}s_6 = 3 \times 0 \\ \\ \pink{\tt \dashrightarrow{}s_6 = 0}$

____________________________________