NCERT Class XI Mathematics - Sequences and Series - Solutions
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Question : 17
Total: 106
In an A.P., the first term is 2 and the sum of the first five terms is one-fourth of the next five terms. Show that 20th term is –112.
Solution:
Let a = 2 be the first term and d be the common difference.
∴ sum of first five termsS 5
=
sum of first ten termsS 10
=
According to question,
Sum of first five terms =
⇒S 5
( s 10 − S 5 ) 4 S 5 S 10 − S 5 5 S 5 S 10
⇒ 5[5(2 + 2d)] = 5(4 + 9d) (From (i) & (ii))
⇒ 25 (2 + 2d)] = 5 (4 + 9d) ⇒ 50 + 50d = 20 + 45d
⇒ 5d = – 30 ⇒ d = – 6
∴t 20
∴ sum of first five terms
=
sum of first ten terms
=
According to question,
Sum of first five terms =
⇒
⇒ 5[5(2 + 2d)] = 5(4 + 9d) (From (i) & (ii))
⇒ 25 (2 + 2d)] = 5 (4 + 9d) ⇒ 50 + 50d = 20 + 45d
⇒ 5d = – 30 ⇒ d = – 6
∴
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