Answer
Verified
400.5k+ views
Hint: In this question, we are given the first 5 numbers of the series and we have to find the next number. Therefore, we should try to find the relation between consecutive numbers, which in this case will give us that the series is an arithmetic progression. Then using the formula for finding the nth term of an AP, ${{a}_{n}}={{a}_{0}}+(n-1)d$ where ${{a}_{0}}$ is the first term and d is the common difference, we can find the next term in the series.
Complete step-by-step answer:
We know that in an arithmetic progression, the next term in a series is obtained by adding a fixed number d to the previous term and d is known as the common difference……………………………………(1.1)
In this question, the first five terms of the series are given as 3, 6, 9, 12, 15. If we take the difference of the consecutive terms, i.e. subtracting the previous term from a term, we get
$\begin{align}
& 5-1=4 \\
& 9-5=4 \\
& 13-9=4 \\
& 17-13=4 \\
\end{align}$
Therefore, we find that each successive term is obtained by adding 4 to the previous term. Therefore, comparing this to (1.1), we find that this series is in an arithmetic progression with common difference 4 and first term 1……………………..(1.2)
We know that the formula for finding the nth term of an arithmetic progression with first term ${{a}_{0}}$ and common difference d is given by
${{a}_{n}}={{a}_{0}}+(n-1)d......................(1.3)$
Therefore, from (1.2), taking ${{a}_{0}}=1$ and $d=4$ and using it in (1.3), we find that the nth term of the given series should be
${{a}_{n}}={{a}_{0}}+(n-1)d=1+\left( n-1 \right)\times 4=1+4n-4=4n-3$
Thus the answer is 4n-3 which matches option (c) of the question. Therefore, (c) should be the correct answer to this question.
Note: As we found that the series is in an arithmetic progression with first term ${{a}_{0}}=1$ and common difference $d=4$ , we should note that we should take (n-1) in equation (1.3) and not n as the difference gets added from the second term, i.e. in the first term, 0 times d is added, in the second term 1 times d is added and so on.
Complete step-by-step answer:
We know that in an arithmetic progression, the next term in a series is obtained by adding a fixed number d to the previous term and d is known as the common difference……………………………………(1.1)
In this question, the first five terms of the series are given as 3, 6, 9, 12, 15. If we take the difference of the consecutive terms, i.e. subtracting the previous term from a term, we get
$\begin{align}
& 5-1=4 \\
& 9-5=4 \\
& 13-9=4 \\
& 17-13=4 \\
\end{align}$
Therefore, we find that each successive term is obtained by adding 4 to the previous term. Therefore, comparing this to (1.1), we find that this series is in an arithmetic progression with common difference 4 and first term 1……………………..(1.2)
We know that the formula for finding the nth term of an arithmetic progression with first term ${{a}_{0}}$ and common difference d is given by
${{a}_{n}}={{a}_{0}}+(n-1)d......................(1.3)$
Therefore, from (1.2), taking ${{a}_{0}}=1$ and $d=4$ and using it in (1.3), we find that the nth term of the given series should be
${{a}_{n}}={{a}_{0}}+(n-1)d=1+\left( n-1 \right)\times 4=1+4n-4=4n-3$
Thus the answer is 4n-3 which matches option (c) of the question. Therefore, (c) should be the correct answer to this question.
Note: As we found that the series is in an arithmetic progression with first term ${{a}_{0}}=1$ and common difference $d=4$ , we should note that we should take (n-1) in equation (1.3) and not n as the difference gets added from the second term, i.e. in the first term, 0 times d is added, in the second term 1 times d is added and so on.
Recently Updated Pages
Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Trending doubts
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE
Select the correct plural noun from the given singular class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
The sum of three consecutive multiples of 11 is 363 class 7 maths CBSE
What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
How many squares are there in a chess board A 1296 class 11 maths CBSE