Question

An AP has eight terms. The sixth term is 15 and the sum of the odd terms is 44. What is the first term?

Answer 1

$\begin{gathered}\sf T Table \\\boxed{\boxed{\red{\begin{array}{ |c |c|c|c|c|c|} \bf\angle A & \bf{0}^{ \circ} & \bf{30}^{ \circ} & \bf{45}^{ \circ} & \bf{60}^{ \circ} & \bf{90}^{ \circ} \\ \\ \rm sin A & 0 & \dfrac{1}{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} &1 \\ \\ \rm cos \: A & 1 & \dfrac{ \sqrt{3} }{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{1}{2} &0 \\ \\ \rm tan A & 0 & \dfrac{1}{ \sqrt{3} }&1 & \sqrt{3} & \rm \infty \\ \\ \rm cosec A & \rm \infty & 2& \sqrt{2} & \dfrac{2}{ \sqrt{3} } &1 \\ \\ \rm sec A & 1 & \dfrac{2}{ \sqrt{3} }& \sqrt{2} & 2 & \rm \infty \\ \\ \rm cot A & \rm \infty & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } & 0 \end{array}}}}\end{gathered}TrigonometryTable∠AsinAcosAtanAcosecAsecAcotA0∘010∞1∞30∘212331232345∘2121122160∘232133223190∘10∞1∞0</p><p>$

Answer 2

Answer:

Here,

a

4

=a+3d

a

8

=a+7d

Therefore,

a+3d+a+7d=24

2a+10d=24

a+5d=12 …… (1)

Again,

a

6

=a+5d

a

10

=a+9d

Therefore,

a+5d+a+9d=44

2a+14d=44

a+7d=22 ……. (2)

Solving equations (1) and (2), we get

d=5 and a=−13

Therefore,

a

1

=a=−13

a

2

=a+d=−13+5=−8

a

3

=a+2d=−13+10=−3