Find the sum of first 15 terms of the AP : 3 , 8 , 13 , 18 , 23 , ....
Answers
Answer:
this is the number sequence right
28, 33, 38, 43 ,48
Given : AP is 3, 8, 13, 18, 23, . . . .
To find : Sum of first 15 terms of AP
Solution :
AP is a sequence of numbers in which common difference between two consecutive terms is always constant everywhere in the sequence.
To find the sum of first n terms of AP, we use the formula :-
- Sn = n/2 [ 2a + ( n - 1 ) d ]
Here,
- Sn = First n natural numbers
- a = First term
- n = Number of terms
- d = Common difference
In the given AP, it is clear that the first term is a = 3.
Common difference can be obtained by subtracting preeceeding term from it's succeeding term.
Common difference, d = a2 - a1 = 8 - 3 = 5
Now since, we have obtained the value of a and d, we can apply formula for sum of 15 terms.
→ Sn = n/2 [ 2a + ( n - 1 ) d ]
→ S15 = 15 / 2 [ 2 ( 3 ) + ( 15 - 1 ) ( 5 ) ]
→ S15 = 15 / 2 [ 6 + ( 14 ) ( 5 ) ]
→ S15 = 15 / 2 [ 6 + 60 ]
→ S15 = 15 / 2 [ 66 ]
→ S15 = 15 × 33
→ S15 = 495
Hence the sum of first 15 terms of the given AP is 495.
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