Question

An arithmetic sequence has first term 25 and common difference 3. Find the 50th
term of the sequence.

Answer 1

Answer:

172

Step-by-step explanation:

The n th term of an arithmetic sequence is

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 25 and d = 3, thus

$a_{50}$ = 25 + (49 × 3) = 25 + 147 = 172

Answer 2

We can use the nth term formula for an arithmetic sequence with d difference or can directly use simple calculations to find the 50th term of given arithmetic sequence.

The 50th term of given sequence is 172.

Given that:

• The first term of the given arithmetic sequence = 25

• The common difference = 3

To find:

The 50th term of the sequence.

Calculations:

Using the formula for nth term of an arithmetic sequence with the first term as a and the common difference d:

$T_n = a + (n-1)d$

Thus, here n = 50, a = 25, d = 3,

$T_{50} = 25 + (50-1)\tiems 3 = 172$

Thus, the 50th term of given arithmetic sequence is 172.

Using general calculation:

Since the first term is 25, and there would be increment of 3 for each next term, thus for 2nd term there'd be increment of 3, for 3rd, it would be 6 and so on. Thus, for 50th term, it would be 3 times (50-1) which is 147.

Thus, 25 added with 147 is 50th term or

50th term is 172.

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