PYQ NEET- Arithmetic Geometric Harmonic Progressions
- The sum of the first 4 terms of an arithmetic progression is 72 and the sum of the first 10 terms is 200. Find the first term and the common difference.
Let a be the first term and d be the common difference of the AP.
We have,
S4 = 72
⇒ 4/2 [2a + 3d] = 72
⇒ 2a + 3d = 36
And,
S10 = 200
⇒ 10/2 [2a + 9d] = 200
⇒ 2a + 9d = 40
Subtracting the second equation from the first, we get
6d = 4
⇒ d = 2
Substituting this value of d in the first equation, we get
2a + 3(2) = 36
⇒ 2a = 30
⇒ a = 15.
Therefore, the first term of the AP is 15 and the common difference is 2.
2
BETA
