if the sum of n terms of an ap is 3 n square + 5 and, then which of its terms is 424
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Answer:417th term
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Answer:
417
Step-by-step explanation:
Sn = 3n² + 5
STEP 1 : Find the First Term:
s1 = 3(1)² + 5 = 8
a1 = s1
a1 = 8
STEP 2: Find the Second Term:
s2 = 3(2)² + 5 = 17
a2 = s2 - s1
a2 = 17 - 8
a2 = 9
STEP 3: Find the common difference
d = a2 - a1
d = 9 - 8
d = 1
STEP 4: Find the nth term of the AP:
a1 = 8, d = 1
an = a1 + (n - 1)(d)
an = 8 + (n - 1)(1)
an = 8 + n - 1
an = n + 7
STEP 5: Find the term that has 424:
an = n + 7
424 = n + 7
n = 424 - 7
n = 417
Answer: It is the 417th term
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