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Basic Adding Patterns in an AP

If a1, a2, a3...

Question

If $a_{1}, a_{2}, a_{3}, a_{4}$ are in AP, then

A

$a_{1} + a_{4} = a_{2} + a_{3}$

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B

$a_{1} + a_{2} = a_{2} + a_{3}$

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C

$a_{1} + a_{2} = a_{3} + a_{4}$

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D

$a_{1} + a_{3} = a_{2} + a_{4}$

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Solution

The correct option is A
$a_{1} + a_{4} = a_{2} + a_{3}$

The sum of the first term and the last term are equal to the sum of the second term and the second last term and so on.
Hence, here $a_{1} + a_{4} = a_{2} + a_{3}$

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Similar questions

a_{1}, a_{2}, a_{3}, a_{4}

are in AP, then

\frac{1}{\sqrt{a_{1}} + \sqrt{a_{2}}} + \frac{1}{\sqrt{a_{2}} + \sqrt{a_{3}}} + \frac{1}{\sqrt{a_{3}} + \sqrt{a_{4}}}

a_{1}

a_{2}

a_{3}

a_{2}

a_{3}

a_{4}

a_{3}

a_{4}

a_{5}

a_{1}

a_{3}

a_{5}

a_{1}, a_{2}, a_{3}, a_{4}, . . {. ., a}_{20}

a_{1} + a_{20} = 45

a_{1} + a_{2} + a_{3} + a_{4}, . . {. . + a}_{20}

a_{1}, a_{2}, a_{3}, a_{4}

are terms of an AP, then the relation between them is

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

a_{4}

a_{1} + a_{4} = 10

a_{2} \cdot a_{3} = 24

, then the least term of them is

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