Question

1. Find the sum of the following APs:
(1) 2, 7, 12,..., to 10 terms.
(ii) 0.6, 1.7, 2.8,..., to 100 terms.​

Answer 1

Answer:

$\mathfrak{\large{ \green{\underline{\underline{Answer}}}}} \\ \large \green{1) = 245} \\ \large \green{2) = 5505}$

Step-by-step explanation:

$\large \green{ \underline{ \underline{to \: find \: the \: sum \: of \: following \: ap}}} \\ \large \green{1) = 2 + 7 + 12 + ......to \: 10 \: terms} \\ \large \green{ \underline{ \underline{formula \: of \: sum \: of \: n \: terms = }}} \\ \large \blue{sn = \frac{n}{2}(2a + (n - 1)d) } \\ \large \blue{ \underline {first \: term = 2}} \\ \large \blue{ \underline{common \: difference = 5}} \\ \large \green{ \underline{ \underline{sum \: of \: 10 \: terms \: of \: ap}}} \\ \large \green{s10 = \frac{10}{2}(2(2) + (10 - 1)5) } \\ \large \green{5(49) = 245} \\ \\ \large \green{2) = 0.6 + 1.7 + 2.8...... \: to \: 100 \: terms} \\ \large \green{s100 = \frac{100}{2}(2(0.6) + (100 - 1)1.1) } \\ \large \green{50(1.2 + 108.9)} \\ \large \green{50(110.1)} \\ \large \green{5505 = answer}$