Question
Download Solution PDFIn an arithmetic progression, the sum of the 3rd, 4th and 5th terms is 12. What is the sum of the first 7 terms?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Arithmetic progression (AP)
Sum of 3rd, 4th, and 5th terms = 12
Formula used:
nth term of an AP: an = a + (n - 1)d
Sum of first n terms of an AP: Sn = (n/2)[2a + (n - 1)d]
Where a is the first term and d is the common difference.
Calculation:
The 3rd, 4th, and 5th terms:
a3 = a + 2d
a4 = a + 3d
a5 = a + 4d
Sum of 3rd, 4th, and 5th terms = 12:
(a + 2d) + (a + 3d) + (a + 4d) = 12
3a + 9d = 12
a + 3d = 4 ... (1)
The sum of the first 7 terms (S7):
S7 = (7/2)[2a + (7 - 1)d]
S7 = (7/2)[2a + 6d]
S7 = 7(a + 3d)
Substitute a + 3d = 4 from equation (1):
S7 = 7 × 4
S7 = 28
∴ The sum of the first 7 terms is 28.
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