Question

4. For an A.P., t1 = 12 and t10 = 102. Find the common difference.
5. Find the sum of first 10 terms of the A.P. 4, 7, 10, ....​

Answer 1

$\bf \large \: ♡Question:1$

$\sf For \: an \: A.P., \: t1 = 12 \: and \: t10 = 102 \\ \sf Find \: t he \: common \: difference.$

$\rightarrow \: t_{10} = t + (n - 1)d$

$\sf \: where \: d \: is \: common \: difference \: </p><p>$

$12 + (10 - 1)d = 102 \\ 9d = 90 \\ \boxed{d = 10}$

$\bf \large \: ♡Question:2$

$\sf \: Find \: the \: sum \: of \: first \\ \sf \: 10 \: terms \: of \: the \: A.P. 4, 7, 10, ....$

$\rightarrow d = a_{2} - a \\ = 7 - 4 \\ \boxed{d = 3} \\ \: s_{10} = \frac{10}{2}(2 + 9d) \\ = 5(2 + 27) \\ \boxed{\boxed{ s_{10} = 145}}$

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