Sum of the first n terms of an AP is 5n2 – 3n. Find the AP and also find its 16th term.
PRIYANSHU1121:
that is 5n2 or 5n square
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In an AP,
Sum of first n terms (Sn) = 5n² - 3n
So,
S1 = 5 × (1)² - 3 × 1 = 5 - 3 = 2
S2 = 5 × (2)² - 3 × 2 = 20 - 6 = 14
S1 = a1 (first term)
S2 = sum of a1 & a2
So,
Second term (a2) = S2 - S1 = 14 - 2 = 12
Common difference (d) = a2 - a1 = 12 - 2 = 10
So,
AP : a, (a + d), (a + 2d), ......
= 2, (2 + 10), (2 + 2 × 10), ....
= 2, 12, 22, ...
Now,
16th term = a + 15d = 2 + 15 × 10 = 2 + 150 = 152
Sum of first n terms (Sn) = 5n² - 3n
So,
S1 = 5 × (1)² - 3 × 1 = 5 - 3 = 2
S2 = 5 × (2)² - 3 × 2 = 20 - 6 = 14
S1 = a1 (first term)
S2 = sum of a1 & a2
So,
Second term (a2) = S2 - S1 = 14 - 2 = 12
Common difference (d) = a2 - a1 = 12 - 2 = 10
So,
AP : a, (a + d), (a + 2d), ......
= 2, (2 + 10), (2 + 2 × 10), ....
= 2, 12, 22, ...
Now,
16th term = a + 15d = 2 + 15 × 10 = 2 + 150 = 152
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