Question

Find the $17^{th}$ term of the arithmetic sequences: 5, 8, 11, 14,….
A. 50
B. 51
C. 52
D. 53

Answer 1

Hint: Here, the given sequence is an A.P. We will use the $n^{th}$ term formula to find the $17^{th}$ of the A.P. First we will find the common difference(d) between two consecutive terms and substitute this value along the first term(a) and ‘n’ as 17 in the $n^{th}$ term of A.P. we will get the required answer.


Complete step-by-step answer:
Given,
Arithmetic sequence 5, 8, 11, 14, ….
$T_n$ = $a + (n-1)d$
where ‘a’ is the first term of the sequence, ‘n’ is the number of terms required to find and ‘d’ is the common difference between the two consecutive terms.
Now the given sequence is 5, 8, 11, 14…....
where, a = 5, n = 17, d = 8 – 5 = 11 – 8 = 3
Now, we will put these values in the formula.
$T_{17}$ = $5 + (17 - 1)3$
$T_{17}$ = $53$
\[\therefore \] $17^{th}$ term of A.P. is 53.

So, the correct answer is “Option D”.

Note: Arithmetic Progression is a series or sequence of numbers in order where the difference between any two consecutive numbers would be the same. For example – the series of even numbers 2, 4, 6, 8, 10 and so on, this is in arithmetic progression because the common difference between two consecutive numbers is constant. In arithmetic progression or sequence every pair of consecutive terms, the second number is obtained by adding a fixed number to the first one. In arithmetic progression, terms are denoted as- $n^{th}$ term is denoted as ${T_n}$, Sum of the first n terms is denoted as ${S_n}$, common difference is denoted as $d$.