In an AP: Given an = 56, d= 7, S₁ = 147 find a and n.
Answers
Answered by
0
Step-by-step explanation:
a
12
=37,d=3
a
12
=a+(12−1)d
37=a+(11×3)
37−33=a
a=4
s
12
=
2
12
[2a+(12−1)3]
s
12
=6[8+33]
s
12
=246
Answered by
6
Answer:
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Step-by-step explanation
Sn = n/2(a + an)
147 = n/2(a +56)
n(a +56 ) = 294 ... (1)
Now
an = a +(n-1)d
56 = a + 7n- 7
a = 63 - 7n ... (2)
Putting (2) in (1), We get
n(119 - 7n) = 294
119n - 7n² = 294
7n² - 119n + 294 = 0
n² - 17n + 42 = 0
n² - 14n - 3n + 42 = 0
n(n-14) - 3 ( n- 14) = 0
(n - 14) (n- 3) = 0
n = 14 or n = 3
If n = 14, then
a = 63 - 7(14)
a = -35
If n = 3, then
a = 63 - 7(3)
a = 42
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