The 13th term of an ap is 4 times its 3rd term. If its 5th term is 16, find the sum of its first 10 terms.
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The 13th term of an ap is 4 times its 3rd term. If its 5th term is 16, find the sum of its first 10 terms.
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an = a1 + (n - 1)d
Find the 13th term:
a13= a + 12d
Find the 3rd term:
a3 = a + 2d
Given that 13th term is 4 times its 3rd term:
a + 12d = 4(a + 2d)
a + 12d = 4a + 8d
3a = 4d ----------------------- [ 1 ]
Given that the 5th term is 16:
16 = a +4d
a = 16 - 4d ----------------------- [ 2 ]
Sub { 2 } into [ 1 ]:
3(16 - 4d) = 4d
48 - 12d = 4d
16d = 48
d = 3 ----------------------- sub into equation [ 2 ]
Find a:
a = 16 - 4d
a = 16 - 4(3)
a = 4
Find the nth term:
an = a1 + (n - 1)d
an = 4 + (n - 1)3
an = 4 + 3n - 3
an = 1 + 3n
Find the 10th term:
a10 = 1 + 3(10)
a10 = 31
Find the sum of the first 10 terms:
Sn = n/2 (a1 + an)
S10 = 10/2 (4 + 31)
S10 = 175
Answer: The sum of the first 10 terms is 175
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Answer:
Hence the sum of first 10 terms is 175.