The sum of 11th term of a.p is 891 find the 28th and 45th term if the common difference is 15
11/2 (2a+10*15) = 891
solve for a, and then you want
a+27d and a+44d
-9
To find the 28th and 45th terms of an arithmetic progression (AP) with a given common difference, we can use the formula for the nth term of an AP.
The nth term of an AP is given by:
𝑎𝑛 = 𝑎₁ + (𝑛 - 1)𝑑
Where:
𝑎𝑛 = nth term of the AP
𝑎₁ = first term of the AP
𝑛 = position of the term
𝑑 = common difference
Given that the 11th term of the AP is 891 and the common difference is 15, we can substitute these values into the formula and solve for 𝑎₁.
891 = 𝑎₁ + (11 - 1) × 15
Simplifying, we have:
891 = 𝑎₁ + 10 × 15
891 = 𝑎₁ + 150
𝑎₁ = 891 - 150
𝑎₁ = 741
Now that we have 𝑎₁, we can find the 28th term using the nth term formula.
𝑎₂₈ = 741 + (28 - 1) × 15
𝑎₂₈ = 741 + 27 × 15
𝑎₂₈ = 741 + 405
𝑎₂₈ = 1146
Therefore, the 28th term of the AP is 1146.
Similarly, we can find the 45th term using the nth term formula.
𝑎₄₅ = 741 + (45 - 1) × 15
𝑎₄₅ = 741 + 44 × 15
𝑎₄₅ = 741 + 660
𝑎₄₅ = 1401
Therefore, the 45th term of the AP is 1401.