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Basic Adding Patterns in an AP

Let a1, a2, …...

Question

Let $a_{1}, a_{2}, \dots$ and $b_{1}, b_{2}, \dots$ be arithmetic progressions such that $a_{1} = 25, b_{1} = 75$ and $a_{100} + b_{100} = 100$ . Find the sum of the first one hundred terms of the progression $a_{1} + b_{1}, a_{2} + b_{2}, \dots$

A

100

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B

10,000

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C

505,000

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D

0

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Solution

The correct option is B 10,000

Option c

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Similar questions

a_{1}, a

b_{1}, b_{2}, . . . .

be the arithmetic progressions such that

a_{1} = 25, b_{1} = 75

a_{1} 00 + b_{100}

. The sum of the first one hundred terms of the progressions

(a_{1} + b_{1}), (a_{2} + b_{2})

, ...... is _______.

a_{1}, a_{2}, a_{3}, . . . . . . . . . . a n d b_{1} b_{2}, b_{3} . . . . . . . . . . .

be arithmetic progression such that

a_{1} = 25, b_{1} = 75 a n d a_{100} + b_{100} = 100

Q. if x is unequal to y and the sequences x,a1,a2,y and x,b1,b2,y are in arithmetic progression what is the value of [a2-a1/b2-b1]

Q. If the points

(a_{1}, b_{1})

(a_{2}, b_{2})

(a_{1} + a_{2}, b_{1} + b_{2})

are collinear, then show that

a_{1} b_{2} = a_{2} b_{1}

b_{i} > 1

i = 1, 2, . . . ., 101

{log}_{e} b_{1} {log}_{e} b_{2}, . . ., {log}_{e} b_{101}

are in Arithmetic Progression (A.P) with the common difference

{log}_{e} 2

a_{1}, a_{2}, . . . a_{101}

are in A.P. such that

a_{1} = b_{1}

a_{51} = b_{51}

t = b_{1} + b_{2} + . . . . + b_{51}

s = a_{1} + a_{2} + . . . . + a_{51}

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