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Let a_1, a and b_1, b_2, .... be the arithmetic progressions s

Question

Let $a_{1}, a$ and $b_{1}, b_{2}, ....$ be the arithmetic progressions such that $a_{1} = 25, b_{1} = 75$ and $a_{1} 00 + b_{100}$ . The sum of the first one hundred terms of the progressions $(a_{1} + b_{1}), (a_{2} + b_{2})$ , ...... is _______.

100

10, 000

5, 05, 000

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Chloe Discussed

Let

a_{1}, a

and

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

be the arithmetic progressions such that

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

and

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 _______.

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Text solutionVerified

Given there are two A.P's

a_{1}, a_{2}, .... an d b_{1}, b_{2}, b_{3} ....

Also given that

a_{1} = 25 an d b_{1} = 75

And the sum of

100

th term of both the A.P is

a_{100} + b_{100} = 100

Given a new A.P:

(a_{1} + b_{1}), (a_{2} + b_{2}), (a_{3} + b_{3}) ...... (a_{100} + b_{100})

∴ a_{1} + b_{1} = 25 + 75 = 100

And the last term is

a_{100} + b_{100} = 100

∴ S_{n} = \frac{n}{2} \times (f i rs t t er m + l a s t t er m) = 50 \times (100 + 100) = 10000

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Question Text	Let $a_{1}, a$ and $b_{1}, b_{2}, ....$ be the arithmetic progressions such that $a_{1} = 25, b_{1} = 75$ and $a_{1} 00 + b_{100}$ . The sum of the first one hundred terms of the progressions $(a_{1} + b_{1}), (a_{2} + b_{2})$ , ...... is _______.
Answer Type	Text solution:1
Upvotes	150