38. Find the sum of the first 15 terms of the AP 12, 17, 22,
Answers
Answer: 705
answer is 705
Given:
AP = 12, 17, 22...
a₁ = 12
d = 17 - 12 = 5
n = 15
To Find:
Sum of the first 15 terms of the AP 12, 17, 22...
Concept:
We apply the formula to find the sum of the first 15 terms. sum of first 15 terms means 12 + 17 + 22...and goes on for 15 terms. this is hard, so to make it easier we will use a formula.
Formula Used:
Sₙ = n/2 (2a₁ + (n - 1) d)
Sₙ = n/2 (2a₁ + (n - 1) d)
= 15/2 [2*(12) + (15-1) 5]
= 15/2 [24 + (14)5]
= 15/2 [24 + 70]
= 15/2 [94]
= 15 * [47] -------94 gets divided by 2 to give 47
= 705
Given,
The AP: 12,17,22,---
To find,
The sum of the first 15 terms of the AP.
Solution,
We can easily solve this problem by following the given steps.
According to the question,
We have:
The AP: 12,17,22,---
The first term (a) = 12
Common difference (d) = second term - first term
d = 17-12
d = 5
We know that the following formula is used to find the sum of n terms of an AP:
Sn = n/2 [2a+(n-1)d]
S15 = 15/2 [2(12)+(15-1)5]
S15 = 15/2 [24+(14)5]
S15 = 15/2 [24+70]
S15 = (15×94)/2
S15 = 15×47
S15 = 705
Hence, the sum of the first 15 terms of 12,17,22,--- is 705.