Answer

Verified

484.2k+ 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

what is the correct chronological order of the following class 10 social science CBSE

Which of the following was not the actual cause for class 10 social science CBSE

Which of the following statements is not correct A class 10 social science CBSE

Which of the following leaders was not present in the class 10 social science CBSE

Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE

Which one of the following places is not covered by class 10 social science CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

Who was the Governor general of India at the time of class 11 social science CBSE

How do you graph the function fx 4x class 9 maths CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Why is there a time difference of about 5 hours between class 10 social science CBSE

Difference Between Plant Cell and Animal Cell