Question

While playing a treasure hunt game, some clues (numbers) are hidden in various spots collectively forms an A.P. If the number on the n spot is 20 + 4n then answer the following questions to help the player in spotting the clues. TREASURE HUNT 1. Find the first 4 terms of this A.P. 2. What is the sum of all the numbers on the first 10 spots?​

Answer 1

Answer:

While playing a treasure hunt game, some clues are hidden in various spots collectively forms

an AP. If the number on the nth spot is 20 + 4, then answer the following questions to help

the player in spotting the clues.

(a) Which number is on the first spot?

(a) 20 (b) 24 (c) 16 (d) 28

(b) Which number is on the ( − 2)th

spot?

(a) 16+4n (b) 24+4n (c) 12+4n (d) 28+4n

(c) Which number is on the 34th spot?

(a) 156 (b) 116 (c) 120 (d) 160

(d) What is the sum of all the numbers on the first 10 spots?

(a) 410 (b) 420 (c) 480 (d) 490

(e) Which spot is numbered as 116?

(a) 5th

(b) 8th

(c) 9th

(d) 24th

Answer 2

Answer: The sum of all the numbers on the first 10 spots is 380.

Step-by-step explanation:

The first 4 terms of this A.P. would be:

20 + 4(1) = 24

20 + 4(2) = 28

20 + 4(3) = 32

20 + 4(4) = 36

To find the sum of all the numbers on the first 10 spots, we can use the formula for the sum of an arithmetic sequence:

$Sum = n/2 (2a + (n-1)d)$

where n is the number of terms, a is the first term, and d is the common difference.

Given that the number on the n spot is $20 + 4n$. So, the first term a = 20 and the common difference d = 4

In this case, we have n = 10 terms.

So, the sum of all the numbers on the first 10 spots would be:

Sum = $10/2 (2(20) + (10-1)(4))$ $= 10/2 (40 + 36)$$= 10/2 (76)$$= 380$

So the sum of all the numbers on the first 10 spots is 380.

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