what is the 17th term from the end of AP 11,16.....211,216.
Answers
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Here is the solution:
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General formula for AP : an = a1 + (n - 1)d
Find a1 and d:
From the series 11, 16, .... 211, 216
⇒ First term = a1 = 11
⇒ Difference = d = 16 - 11 = 5
Find the AP in term of n:
an = a1 + (n - 1)d
an = 11 + ( n - 1)5
an = 11 + 5n - 5
an = 6 + 5n
Find n for the last term 216:
an = 6 + 5n
216 = 6 + 5n
5n = 216 - 6
5n = 210
n = 210 ÷ 5 = 42
There are 42 terms
Find the 17th term from the end:
There are 42 terms
17th term from the end = 42 - 17 + 1 = 26th
Find the 26th term:
a26= 6 + 5(26) = 136
Answer: The 17th term is 136
given AP:11,16,........211,216
reverse of AP=216,211,......,16,11
a=216,d=211-216=-5,n=17,an=?
an=a+(n-1)d
an=216+(17-1)(-5)
an=216+(16)(-5)
an=216-80
an=136
∴17th term of given AP is 136.
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