Answer
Verified
426.9k+ views
Hint- First find out the type of progression which the sequence is in that is if it is in A.P, G.P or H.P and solve it.
The series given to us is 3.75,3.5,3.25…………..
We have been asked to find out the sum of the series upto 16 terms
From the series given we get ${T_2} - {T_1} = 3.5 - 3.75 = - 0.25$
Also, we get ${T_3} - {T_2} = 3.25 - 3.50 = - 0.25$
So, from this we got ${T_3} - {T_2} = {T_2} - {T_1}$ =common difference=d
So, from this we can conclude that the given series is in Arithmetic Progression(A.P)
So, we know that the sum of n terms of an A.P is given by
${S_n} = \dfrac{n}{2}\left[ {2a + \left( {n - 1} \right)d} \right]$
So, on comparing with the sequence ,we can write
The first term=a=3.75
Common difference d=-0.25
Here, since we have to find out the sum upto 16 terms, we consider n=16
Let us substitute these values in the ${S_n}$ formula
So, we get $
{S_{16}} = \dfrac{{16}}{2}\left( {2 \times 3.75 + (16 - 1)( - 0.25)} \right) \\
{S_{16}} = 8(7.5 - 3.75) \\
{S_{16}} = 8(3.75) \\
\Rightarrow{S_{16}} = 30 \\
$
So, the sum of the series upto 16 terms=30
Note: When finding sum to n terms of an AP we can make use of an alternative formula if the first and last terms of an AP are known or we can use the same formula as used in this problem and solve.
The series given to us is 3.75,3.5,3.25…………..
We have been asked to find out the sum of the series upto 16 terms
From the series given we get ${T_2} - {T_1} = 3.5 - 3.75 = - 0.25$
Also, we get ${T_3} - {T_2} = 3.25 - 3.50 = - 0.25$
So, from this we got ${T_3} - {T_2} = {T_2} - {T_1}$ =common difference=d
So, from this we can conclude that the given series is in Arithmetic Progression(A.P)
So, we know that the sum of n terms of an A.P is given by
${S_n} = \dfrac{n}{2}\left[ {2a + \left( {n - 1} \right)d} \right]$
So, on comparing with the sequence ,we can write
The first term=a=3.75
Common difference d=-0.25
Here, since we have to find out the sum upto 16 terms, we consider n=16
Let us substitute these values in the ${S_n}$ formula
So, we get $
{S_{16}} = \dfrac{{16}}{2}\left( {2 \times 3.75 + (16 - 1)( - 0.25)} \right) \\
{S_{16}} = 8(7.5 - 3.75) \\
{S_{16}} = 8(3.75) \\
\Rightarrow{S_{16}} = 30 \\
$
So, the sum of the series upto 16 terms=30
Note: When finding sum to n terms of an AP we can make use of an alternative formula if the first and last terms of an AP are known or we can use the same formula as used in this problem and solve.
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
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Summary of the poem Where the Mind is Without Fear class 8 english CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Write an application to the principal requesting five class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE