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The sum of the first 16 terms of an AP whose first term and third term are 5 and 15 respectively is
- a)600
- b)765
- c)640
- d)680
- e)690
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The sum of the first 16 terms of an AP whose first term and third term...
1st Method:
1st term = 5;
3rd term = 15;
Then, d = 5;
16th term = a+15d = 5+15*5 = 80;
Sum = {n*(a+L)/2} = {No. of terms*(first term + last term)/2}.
Thus, sum = {16*(5+80)/2} = 680.
2nd Method (Thought Process):
Sum = Number of terms * Average of that AP.
Sum = 16* {(5+80)/2} = 16*45 = 680.
Most Upvoted Answer
The sum of the first 16 terms of an AP whose first term and third term...
Problem: Find the sum of the first 16 terms of an AP whose first term and third term are 5 and 15 respectively.
Solution:
We are given the first term (a) and the third term (c) of an AP. We need to find the sum of the first 16 terms of this AP.
Let the common difference be d. Then we have:
c = a + 2d (since the third term is obtained by adding 2d to the first term)
Substituting the given values, we get:
15 = 5 + 2d
10 = 2d
d = 5
Now we can find the sum of the first 16 terms using the formula:
Sn = n/2[2a + (n-1)d]
where Sn is the sum of the first n terms of the AP.
Substituting the values, we get:
S16 = 16/2[2(5) + (16-1)(5)]
S16 = 8[10 + 75]
S16 = 680
Therefore, the sum of the first 16 terms of the given AP is 680.
Answer: (d) 680
Solution:
We are given the first term (a) and the third term (c) of an AP. We need to find the sum of the first 16 terms of this AP.
Let the common difference be d. Then we have:
c = a + 2d (since the third term is obtained by adding 2d to the first term)
Substituting the given values, we get:
15 = 5 + 2d
10 = 2d
d = 5
Now we can find the sum of the first 16 terms using the formula:
Sn = n/2[2a + (n-1)d]
where Sn is the sum of the first n terms of the AP.
Substituting the values, we get:
S16 = 16/2[2(5) + (16-1)(5)]
S16 = 8[10 + 75]
S16 = 680
Therefore, the sum of the first 16 terms of the given AP is 680.
Answer: (d) 680
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The sum of the first 16 terms of an AP whose first term and third term are 5 and 15 respectively isa)600b)765c)640d)680e)690Correct answer is option 'D'. Can you explain this answer?
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