Answer
Verified
408.9k+ views
Hint: We can use sum of n terms of an arithmetic progression i.e. \[{{S}_{n}}=\dfrac{n}{2}[2a+(n-1)d]\]
Where ${{S}_{n}}$ is the sum of n terms of an A.P
n is the number of terms
a is the first term of A.P
d is a common difference of two consecutive terms.
Complete step-by-step solution -
Explanation:
We know that sum of n terms of an arithmetic progression whose term is ‘a’ and common difference ‘d’ is given by
\[{{S}_{n}}=\dfrac{n}{2}[2a+(n-1)d]\]
In given question \[a=3,n=8,{{S}_{8}}=192\]
So we can write
\[\Rightarrow 192=\dfrac{8}{2}[2\times 3+(8-1)d]\]
\[\Rightarrow 192=4[6+7d]\]
\[\Rightarrow \dfrac{192}{4}=6+7d\]
\[\Rightarrow 48=6+7d\]
\[\Rightarrow 48-6=7d\]
\[\Rightarrow 42=7d\]
\[\Rightarrow d=\dfrac{42}{7}=6\]
So, \[d=6\].
Hence the value of common difference ‘d’ is 6.
Note: We need to be careful about the formula. In arithmetic, we have two formulas for finding sum as below
${{S}_{n}}=\dfrac{n}{2}\left[ 2a+(n-1)d \right]=\dfrac{n}{2}(a+l)$
So in this, if we will use the formula for the last term, here we will have to find the value of last terms due to which the solution will become lengthy and complicated.
Where ${{S}_{n}}$ is the sum of n terms of an A.P
n is the number of terms
a is the first term of A.P
d is a common difference of two consecutive terms.
Complete step-by-step solution -
Explanation:
We know that sum of n terms of an arithmetic progression whose term is ‘a’ and common difference ‘d’ is given by
\[{{S}_{n}}=\dfrac{n}{2}[2a+(n-1)d]\]
In given question \[a=3,n=8,{{S}_{8}}=192\]
So we can write
\[\Rightarrow 192=\dfrac{8}{2}[2\times 3+(8-1)d]\]
\[\Rightarrow 192=4[6+7d]\]
\[\Rightarrow \dfrac{192}{4}=6+7d\]
\[\Rightarrow 48=6+7d\]
\[\Rightarrow 48-6=7d\]
\[\Rightarrow 42=7d\]
\[\Rightarrow d=\dfrac{42}{7}=6\]
So, \[d=6\].
Hence the value of common difference ‘d’ is 6.
Note: We need to be careful about the formula. In arithmetic, we have two formulas for finding sum as below
${{S}_{n}}=\dfrac{n}{2}\left[ 2a+(n-1)d \right]=\dfrac{n}{2}(a+l)$
So in this, if we will use the formula for the last term, here we will have to find the value of last terms due to which the solution will become lengthy and complicated.
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
Assertion CNG is a better fuel than petrol Reason It class 11 chemistry CBSE
How does pressure exerted by solid and a fluid differ class 8 physics CBSE
Number of valence electrons in Chlorine ion are a 16 class 11 chemistry CBSE
What are agricultural practices? Define
What does CNG stand for and why is it considered to class 10 chemistry CBSE
The rate of evaporation depends on a Surface area b class 9 chemistry CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
State whether the following statement is true or false class 11 physics CBSE
A night bird owl can see very well in the night but class 12 physics CBSE