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| 1. |
The first term of ap is 5 |
| Answer» Here, a = 5l = 45S = 400We know that{tex}S = \\frac{n}{2}(a + l){/tex}{tex} \\Rightarrow 400 = \\frac{n}{2}(5 + 45){/tex}{tex} \\Rightarrow 400 = \\frac{n}{2}(50){/tex}{tex} \\Rightarrow 400 - 25n{/tex}{tex} \\Rightarrow n = \\frac{{400}}{{25}}{/tex}{tex} \\Rightarrow n = 16{/tex}Hence, the number of terms is 16.Again, we know thatl = a + (n - 1)d{tex} \\Rightarrow {/tex}\xa045 = 5 + (16 - 1)d{tex} \\Rightarrow {/tex}\xa045 = 5 + 15d{tex} \\Rightarrow {/tex}\xa040 = 15 d{tex} \\Rightarrow d = \\frac{{40}}{{15}} = \\frac{8}{3}{/tex}Hence, the common difference is\xa0{tex}\\frac{8}{3}{/tex}. | |