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Common Difference

If a 1, a 2, ...

Question

If $a_{1}, a_{2}, a_{3}$ .... a_{n} are in A. P., then the common difference is--

A

a_{2} - a_{1}

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B

a_{4} - a_{3}

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C

a_{n} - a_{n - 1}

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D

a_{7} - a_{6}

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Solution

The correct options are
A $a_{2} - a_{1}$
B $a_{4} - a_{3}$
C $a_{n} - a_{n - 1}$
D $a_{7} - a_{6}$
We know if some no. are in A. P., then the difference between any term and the term preceding to it will be constant, this difference is known as common difference. Here, in the options we can see that the difference between a term and a term preceding to it is given so all the options are correct.

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Similar questions

a_{1}, a_{2}, a_{3}

.... a_{n} are in A. P., then the common difference is--

a_{1}, a_{2}, a_{3}, . . . . . . . a_{n}

are first n terms of an A.P. with first term

a_{1} = 0

and common difference

d \neq 0

\frac{a_{3} - a_{2}}{a_{2}} + \frac{a_{4} - a_{2}}{a_{3}} + \frac{a_{5} - a_{2}}{a_{4}} . . . . . . . . . . . . \frac{a_{n} - a_{2}}{a_{n - 1}}

a_{1}, a_{2}, a_{3}, \dots, a_{n}

are in A.P. and

a_{1} + a_{4} + a_{7} + \dots + a_{16} = 114

a_{1} + a_{6} + a_{11} + a_{16}

a_{1}, a_{2}, a_{3}, \dots

is an arithmetic progression with common difference 1 and

a_{1} + a_{2} + a_{3} + \dots \dots + a_{98} = 137

, then what is the value of

a_{2} + a_{4} + a_{6} + \dots \dots + a_{98}

Q. For an A.P.,

a_{1}, a_{2}, a_{3}, \dots \dots

a_{3} + a_{5} + a_{8} = 11

a_{4} + a_{2} = - 2

, then the value of

a_{1} + a_{6} + a_{7}

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