Question

1) The first term of an AP.is -2 and the 10 term is 16. Determine the 15 term​

Answer 1

GIVEN:

• first term (a) of an AP = -2
• 10th term of an A.P = 16

TO FIND:

• Determine the 15th term ?

SOLUTION:

We have the first term of an AP .is -2 and the 10 term is 16.

➨ $\sf{ {a}_{10} }$ = 16

According to question:-

➨ a + 9d = 16

We know the value of a is –2

➨ –2 + 9d = 16

➨ 9d = 16+2

➨ 9d = 18

➨ d = $\sf{ \cancel\dfrac{18}{9}}$

❮ d = 2 ❯ 

We have to find the 15th term

➨ 15th term = a + 14d

➨ 15th term = –2 + 14 $\times$ 2

➨ 15th term = –2 + 28

❮ 15th term = 26 ❯ 

❝ Hence, the 15th term of an A.P. is 26 ❞

______________________

Answer 2

Explanation.

First term of an Ap = -2

10th term = 16

Determine 15th term

Formula of nth term of Ap

An = a + ( n - 1 ) d

T10 = a + 9d = 16

-2 + 9d = 16

9d = 18

d = 2

15th term

T15 = a + 14d

-2 + 14(2)

-2 + 28

26

Therefore,

15th term = 26

More information

Nth term of an Ap

$\bold{a_{n} = a + (n - 1)d}$

sum of nth term of an Ap

$\bold{s_{n} \: = \frac{n}{2}(2a + (n - 1)d)}$