Question

Find the 75th term of the arithmetic sequence -1, 15, 31, ...−1,15,31,

Answer 1

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☆ Given Arithmetic sequence:-

• -1, 15, 31.....

☆ To find:-

• 75th term.

☆ Formula used:-

an = a+(n-1)d,

Where n is number of terms, a is first term, and d is common difference.

☆ Here,

Common Difference(d),

= Second term - First term.

= 15 - (-1).

= 15 + 1.

${\large{\blue{\boxed{\bold{=\:16}}}}}$

☆ Therefore 75th term,

= (-1) + (75-1)(16)

= -1 + (74)(16)

= -1 + 1184

${\large{\red{\boxed{\bold{=\:1183}}}}}$

Therefore 75th term of the given Arithmetic Sequence is 1183.

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Answer 2

75th term of Arithmetic sequence is 1183

Given:

-1, 15, 31,... is Arithmetic series

To find:

The 75th term of the arithmetic sequence -1, 15, 31, ...

Solution:

Given that

-1, 15, 31,... is Arithmetic series  

Here first term a = -1

Common difference = 2nd term - 1st term

= 15 - (-1) = 15 + 1 = 16

⇒ common difference d = 16

As we know nth term of a sequence  a$_{n}$ = a+(n-1)d

⇒ 75th term, a₇₅ = a + (75-1)d = a + 74d

⇒ a + 74d  = -1 + 74(16) = -1 + 1184  = 1183

75th term of Arithmetic sequence = 1183

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