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Question
Which term of the AP: –2, –7, –12,... will be –77? Find the sum of this AP upto the term –77.
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Solution
Given, AP: –2, –7, –12,...
Let the nth term of an AP is –77
Then, first term (a) = –2 and
Common difference (d) = –7 – (–2)
= –7 + 2
= –5
∵ nth term of an AP, Tn = a + (n – 1)d
⇒ –77 = –2 + (n – 1)(–5)
⇒ –75 = –(n – 1) × 5
⇒ (n – 1) = 15
⇒ n = 16
So, the 16th term of the given AP will be –77
Now, the sum of n terms of an AP is
Sn = `n/2[2a + (n - 1)d]`
So, sum of 16 terms i.e., upto the term –77
S16 = `16/2 [2 xx (-2) + (n - 1)(-5)]`
= 8[–4 + (16 – 1)(–5)]
= 8(–4 – 75)
= 8 × (–79)
= –632
Hence, the sum of this AP upto the term –77 is –632.
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