Question

4)
Find the sum of the first three terms of the A.P. 3,5,7,9,
a. 8
b. 14
d. 24
C. 15​

Answer 1

Given

$\tt \to \: 3,5,7,9,$

$\tt \to \: first \: term(a) = 3$

$\tt \to \: common \: difference(d) = a _{2} - a_{1} = 5 - 3 = 2$

$\tt \to \: Number \: of \: terms(n) = 3$

Formula

$\tt \to \:S_n = \dfrac{n}{2} \{2a + (n - 1)d \}$

$\tt \to \: S_3 = \dfrac{3}{2} \{2 \times 3 + (3 - 1) \times 2 \}$

$\tt \to \: S_ 3 = \dfrac{3}{2} \{6 + 2 \times 2 \}$

$\tt \to \: S_ 3 = \dfrac{3}{2} \{6 +4 \}$

$\tt \to \: S_ 3 = \dfrac{3}{2} \{10 \}$

$\tt \to \: S_ 3 = {3}{} \times 5 = 15$

Answer

$\tt \to \: S_ 3 = 15$

Answer 2

Answer:

Given :-

• A.P = 3 , 5 , 7 , 9

To Find :-

• What is the sum of the first three terms of A.P.

Formula Used :-

$\longmapsto \sf\boxed{\bold{\pink{S_n =\: \dfrac{n}{2}\bigg[2a + (n - 1)d\bigg]}}}$

where,

• $\sf S_n$ = Sum of n terms
• a = First term of A.P
• d = Common difference of A.P

Solution :-

Given :

• First term (a) = 3
• Common difference (d) = 5 - 3 = 2
• Sum of n terms (n) = 3

According to the question by using the formula we get,

$\implies \sf S_3 =\: \dfrac{3}{2}\bigg[2(3) + (3 - 1)2\bigg]$

$\implies \sf S_3 =\: \dfrac{3}{2}\bigg[3 \times 2 + 2 \times 2\bigg]$

$\implies \sf S_3 =\: \dfrac{3}{2}\bigg[6 + 4\bigg]$

$\implies \sf S_3 =\: \dfrac{3}{2}\bigg[10\bigg]$

$\implies \sf S_3 =\: \dfrac{3}{\cancel{2}} \times {\cancel{10}}$

$\implies \sf S_3 =\: 3 \times 5$

$\implies \sf\bold{\red{S_3 =\: 15}}$

$\therefore$ The sum of the first three terms of A.P. 3 , 5 , 7 , 9 is 15 .

Hence, the correct options is option no (C) 15 .

$\rule{150}{2}$

Important Formula :-

$\mapsto \sf \bold{\green{a_n =\: a(n - 1)d}}$

where,

• $\sf a_n$ = nth term of the sequence
• a = First term of the sequence
• d = Common difference