Question

the sum of n terms of AP is 90.the first term is 2 and common difference is 8.find the number of terms

Answer 1

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Here is ur answer ⬇️
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First term (a) = 2
Common difference (d) = 8
Sn = 90
Number of terms (n) = ????
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So,
Sn = n/2 [2a + (n-1)d]
90 = n/2[2(2) + (n-1)8]
180 = n [4 + 8n - 8]
180 = n[ 8n - 4]
180 = 8n^2 - 4n
180 = 4(2n^2 - n ]
180/4 = [2n^2 - n]
45 = 2n^2 - n
0 = 2n^2 - n - 45
0 = 2n^2 - 10n + 9n - 45
0 = 2n( n-5) + 9(n- 5)
0 = (2n+9) (n-5)

So, 2n+9 =0
n = -9/2
& n - 5 = 0
n = 5
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SO, NUMBER OF TERMS OF AN A.P. IS 5✔✔
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