Question

Find the 30th term of the A. P. 3, 8, 13, …, 253.

Answer 1

We need to find the 30 th term of the given A. P. So, in order to calculate the 30th term, we will use the formula to find the nth term of a given A. P.

Complete step-by-step answer:
Here, we are given the arithmetic progression A. P. 3, 8, 13, ..., 253.
We need to calculate the 30th term of this A. P.
We know that nth term of the A. P. is given by the formula: $T_n$ = a+(n-1) d
where, Tn: nth term of the given A. P.
a: 1st term of the given A. P.
d: common difference of the given A. P. = $T_n$ - $T_(n-1)$
Here, we are given that in the given A. P., we have n = 30, a = 3 and d = 5
Putting all these values of n, a and d in the formula of Tn, we get
$T_{30}$= 3 + (30 – 1) 5
= 3 + (29) 5
= 3 + 145 = 148
Therefore, 30th term of the given A. P. 3, 8, 13, …, 253 is found to be 148.

Note: In such problems where we are required to find any term of the A.P. we just substitute the values that are given in the questions into the formula to find the nth term of the A.P. In these problems, you might get confused in the formulae, so memorise the formulae .