The sum of the first 7 terms of an A.P. is 63 and the sum of its next 7 terms is 161. Find the 28th term of this A.P.
Answers
Answer:
28th term of this A.P is 57.
Step-by-step explanation:
Given :
S7 = 63 and sum of its next 7 terms is 161
By using the formula ,Sum of nth terms , Sn = n/2 [2a + (n – 1) d]
S7 = (7/2) [ 2a + (7 - 1)d ]
63 = 7/2 [2a + 6d]
63 × 2/7 = [2a + 6d]
9 × 2 = 2a + 6d
2a + 6d = 18 ………...(1)
And
Sum of its next 7 terms = 161(Given)
Sum of first 14 terms = Sum of first 7 terms + Sum of next 7 terms.
S14 = 63 + 161 = 224
S14 = 224
By using the formula ,Sum of nth terms , Sn = n/2 [2a + (n – 1) d]
S14 = (14/2) [ 2a + (14 - 1)d ]
224 = 7 [ 2a + 13d ]
224/7 = 2a + 13d
2a + 13d = 32 ………... (2)
On subtracting eq (1) from (2)
2a + 13d = 32
2a + 6d = 18
(-) (-) (-)
-------------------
7d = 14
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d = 14/7
d = 2
On putting the value of d = 2 in eq (1),
2a + 6d = 18
2a + 6(2) = 18
2a + 12 = 18
2a = 18 - 12
2a = 6
a = 6/2
a = 3
For 28th term :
By using the formula ,an = a + (n - 1)d
a28 = a + ( 28 - 1) d
a28 = 3 + (27) 2
a28 = 3 + 54
a28 = 57
Hence, 28th term of this A.P is 57.
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Step-by-step explanation:
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