Question

Find the 30th term of the sequence?
1/2, 1, 3/2......
​

Answer 1

Answer:

Step-by-step explanation:

Common Difference = (1-1/2) 1/2

then by using the equation

nth terms= a+c.d(n-1)

= 1/2+ (30-1)1/2

= 1/2 + (29)/2

= 30/2

= 15

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Answer 2

Information provided with us:

• Sequence is 1/2, 1, 3/2...

What we have to calculate:

• 30 term of the above seqúence which we have already got

Using Formula:

• t_n = a + (n - 1) d

Where,

• t is n^th term
• a is first term
• d is common difference
• n is no. of terms

Finding out common difference (d):

• Here we can obtain it by substracting 1/2 with 1

➺ D = 1/1 - 1/2

➺ D = 1 × 2/1 × 2 - 1/2

➺ D = 2 / 2 - 1/2

➺ D = 2 - 1 / 2

➺ D = 1/2

Therefore, common difference is 1/2!

Given:

• No. of terms (n) is 30

Now we would have,

• a = 1/2
• d = 1/2
• n = 30

Putting the values in the formula,

➺ t_n = 1/2 + (30 - 1) 1/2

➺ t_n = 1/2 + (29) 1/2

➺ t_n = 1/2 + 29 × 1/2

➺ t_n = 1/2 + 29 × 1 / 2

➺ t_n = 1/2 + 29/2

➺ t_n = 1+29 / 2

➺ t_n = 30/2

➺ t_n = 15

Henceforth, 30th term of the séquence is 15!

More to learn:

• Arithmetic progression (A.P.) is a sequence in which each term can be found by adding a certain quantity to its preceding term
• Difference between two consecutive terms is called common difference
• Progression means it's a type of sequence in which each term is related to its predecessor and successor.

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