Question

1. If the first term of an AP is -5 and the common difference is 2, then the sum of the first 6 terms is * 2 points (A) 15 (B) 5 (C) 0 (D) 11

Answer 1

$\large\bf\underline{Given:-}$

• First term = -5
• common difference = 2

$\large\bf\underline {To \: find:-}$

• Sum of 1st 6 terms

$\huge\bf\underline{Solution:-}$

• $\blacktriangleright$ First term (a) = -5
• $\blacktriangleright$ Common difference (d) = 2

we know that,

$\large\bullet \: \bf s_n = \frac{n}{2} \big \{ 2a + (n - 1)d \big\}$

▶️ Sum of first 6 terms :-

$\large \rightarrowtail \tt \: s _{6} = \frac{6}{2} \{2 \times - 5 +5 \times 2 \} \\ \\ \large \rightarrowtail \tt \: s _{6} = 3 \{ - 10 + 10 \} \\ \\ \large \rightarrowtail \tt \: s _{6} = 3 \{0 \} \\ \\ \large \rightarrowtail \tt \: s _{6} = 0$

So,

Sum of first 6 terms is 0.

therefore ,

• option (C) = 0 is correct

━━━━━━━━━━━━━━━━━━━

Some formulas related to AP.

»★ $\large\tt{a_n = a+ (n-1)d}$

»★ $\large\bf s_n = \frac{n}{2} \{ 2a + (n - 1)d \}$

»★ $\large\bf s_n = \frac{n}{2} \{ a +a_n \}$

Where,

• ≫ a = first term
• ≫ d = common difference
• ≫ an = nth term
• ≫ n = number of terms

Answer 2

✥ Given ✥

The first term of an AP is -5 and the common difference is 2.

☛ a₁ = -5

☛ d = 2

✥ To Find ✥

If the sum of the first 6 terms of the AP is

(A) 15

(B) 5

(C) 0

(D) 11

✥ Solution ✥

We know, for n terms in AP -

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

⇢ Substituting the values :-

$\sf{\to S_6=\dfrac{6}{2} [2(-5)+(6-1)2)]}\\\\\sf{\to S_6=3[-10+(5\times2)]}\\\\\sf{\to S_6=3(-10+10)}\\\\\sf{\to S_6=3\times0}\\\\\boxed{\boxed{\color{lime}{\sf{\to S_6=0}}}}$

Therefore, the answer is (C) 0.

$\rule{180}2$

For the last term of the AP given, the sum can also be calculated as follows :-

$\sf{S_n=\dfrac{n}{2}(a+l)}$

Where,

➨ a is the first term of the AP, and

➨ l is the last term of the AP.