Question

X, 2X + 11 and 4X - 3 are consecutive terms of an arithmetic sequence. Find the constant difference between terms. Give a formula for finding the nth term of the sequence. Use your formula to find the 27th term of this sequence.

Answer 1

Common difference between the terms is 36

Formula for nth term is $a_n=36n-11$

27th term is 961

Given :

X, 2X + 11 and 4X - 3 are consecutive terms of an arithmetic sequence

To Find:

We need to find the constant difference between the given terms and also find the nth term . Also find the 27th term .

To find the difference , we need to take the difference of consecutive terms

$2x+11-x=x+11\\\\4x-3=(2x+11)= 4x-3-2x-11=2x-14$

Both the common differences are equal

$x+11=2x-14\\Solve \; for \; x\\Subtract \; x\\11=x-14\\Add \; 14\\x=25$

First term is 25

second term is 2(25)+11=61

Difference is 61-25=26

Common difference = 36

Use nth term formula is

$a_n=a+(n-1)d\\a=25 (first term )\\d=36\\a_n=25+(n-1)(36)\\a_n=25+36n-36\\a_n=36n-11$

To find 27th term , replace n with 27

$a_{27}=36(27)-11=961$

Learn more :  brainly.in/question/41142594