Answer
Verified
418.8k+ views
Hint: - ${n^{th}}$term of an A.P is given as$\left( {{a_n} = {a_1} + \left( {n - 1} \right)d} \right)$, (where d is the common difference)
Given data:
First term of an A.P$\left( {{a_1}} \right) = 2$……………… (1)
Sum of first five terms $\left( {{S_5}} \right) = 5$……………… (2)
Then we have to find out the value of ${\text{3}}{{\text{1}}^{st}}$term.
Now, we know that the sum of an A.P is
${{\text{S}}_n} = \dfrac{n}{2}\left( {2{a_1} + \left( {n - 1} \right)d} \right)$, (where d is the common difference)
So, ${{\text{S}}_5} = \dfrac{5}{2}\left( {2{a_1} + \left( {5 - 1} \right)d} \right)$
Now from equation (1) and (2) we have
$
{{\text{S}}_5} = \dfrac{5}{2}\left( {2{a_1} + \left( {5 - 1} \right)d} \right) \\
\Rightarrow 5 = \dfrac{5}{2}\left( {2 \times 2 + 4d} \right) \\
\Rightarrow 2 = 4 + 4d \\
\Rightarrow d = \dfrac{{2 - 4}}{4} = \dfrac{{ - 2}}{4} = \dfrac{{ - 1}}{2} \\
$
Now, we have to find out the value of ${\text{3}}{{\text{1}}^{st}}$term.
As we know that the ${n^{th}}$term of an A.P is given as$\left( {{a_n} = {a_1} + \left( {n - 1} \right)d} \right)$
$ \Rightarrow {31^{th}}$Term of the A.P is
$ \Rightarrow {a_{31}} = 2 + \left( {31 - 1} \right)\left( {\dfrac{{ - 1}}{2}} \right) = \left( {2 - 15} \right) = - 13$
So, option (c) is correct.
Note: - In such types of questions the key concept we have to remember is that always remember all the general formulas of A.P which is stated above, then first find out the value of common difference using the formula of sum of an A.P then using the formula of ${n^{th}}$term of an A.P calculate the value of ${31^{th}}$term which is the required answer.
Given data:
First term of an A.P$\left( {{a_1}} \right) = 2$……………… (1)
Sum of first five terms $\left( {{S_5}} \right) = 5$……………… (2)
Then we have to find out the value of ${\text{3}}{{\text{1}}^{st}}$term.
Now, we know that the sum of an A.P is
${{\text{S}}_n} = \dfrac{n}{2}\left( {2{a_1} + \left( {n - 1} \right)d} \right)$, (where d is the common difference)
So, ${{\text{S}}_5} = \dfrac{5}{2}\left( {2{a_1} + \left( {5 - 1} \right)d} \right)$
Now from equation (1) and (2) we have
$
{{\text{S}}_5} = \dfrac{5}{2}\left( {2{a_1} + \left( {5 - 1} \right)d} \right) \\
\Rightarrow 5 = \dfrac{5}{2}\left( {2 \times 2 + 4d} \right) \\
\Rightarrow 2 = 4 + 4d \\
\Rightarrow d = \dfrac{{2 - 4}}{4} = \dfrac{{ - 2}}{4} = \dfrac{{ - 1}}{2} \\
$
Now, we have to find out the value of ${\text{3}}{{\text{1}}^{st}}$term.
As we know that the ${n^{th}}$term of an A.P is given as$\left( {{a_n} = {a_1} + \left( {n - 1} \right)d} \right)$
$ \Rightarrow {31^{th}}$Term of the A.P is
$ \Rightarrow {a_{31}} = 2 + \left( {31 - 1} \right)\left( {\dfrac{{ - 1}}{2}} \right) = \left( {2 - 15} \right) = - 13$
So, option (c) is correct.
Note: - In such types of questions the key concept we have to remember is that always remember all the general formulas of A.P which is stated above, then first find out the value of common difference using the formula of sum of an A.P then using the formula of ${n^{th}}$term of an A.P calculate the value of ${31^{th}}$term which is the required answer.
Recently Updated Pages
Assertion The resistivity of a semiconductor increases class 13 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE
Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE
What are the possible quantum number for the last outermost class 11 chemistry CBSE
Is C2 paramagnetic or diamagnetic class 11 chemistry CBSE
Trending doubts
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE
Which type of bond is stronger ionic or covalent class 12 chemistry CBSE
What organs are located on the left side of your body class 11 biology CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
How fast is 60 miles per hour in kilometres per ho class 10 maths CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
When people say No pun intended what does that mea class 8 english CBSE