QQuestion
The first term of an Arithmetic Progression is 5, the last term is 50 and the sum is 440. Find:
(a) the number of terms.
(b) the common difference.
ICSEClass XMathematicsArithmetic And Geometric Progression03 Mark2025 Moderate
✓Answer
First term, a = 5
Last term, l = 50
Sum, Sₙ = 440
(a) \mathrm{S}_{\mathrm{n}}=\frac{\mathrm{n}}{2}(\mathrm{a}+\mathrm{l})
440 = \frac{\mathrm{n}}{2}(5 + 50)
⇒ 440=\frac{55\mathrm{n}}{2}
⇒ 880 = 55n
⇒ n = 16
(b) l = a + (n − 1)d
50 = 5 + (16 − 1)d
⇒ 50 = 5 + 15d
⇒ 45 = 15d
⇒ d = 3
Therefore, the number of terms is 16 and the common difference is 3.
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