Question

Find the 16th term of an A.P., whose 1st term is 15 and common difference is -2.

Answer 1

Answer:

A.P. is 2

Step-by-step explanation:

Let d is common difference of AP

Now first 4 terms are 5, 5+d, 5+2d, 5+3d

and next 4 terms 5+4d, 5+5d, 5+6d, 5+7d

Given that, the sum of its first four terms is half the sum of the next four terms.

i.e.,

5 + 5+d + 5+2d + 5+3d=

2

5+4d + 5+5d + 5+6d + 5+7d

20+6d=

2

(20+22d)

20+6d=10+11d

d=2

Hence, the common difference of the given A.P. is 2

Answer 2

Answer:

• $\bold{T_{16}=-15}$

Step-by-step explanation:

Given :

• First term of an A.P (a) = 15.
• Common difference (d) = -2.

To find :

• 16th term of the A.P.

Solution :

$\rightarrowtail \bold{nth\;term\;of\;an\;A.P\;is\;given\;as:}$

• $\bold{a+(n-1)d}$

$\Rightarrow \bold{T_{16}=15+(16-1)-2}$

$\Rightarrow \bold{T_{16}=15+(15)-2}$

$\Rightarrow \bold{T_{16}=15+(-30)}$

$\Rightarrow \bold{T_{16}=15-30}$

$\twoheadrightarrow \bold{T_{16}=-15}$

∴ 16th term of the A.P is -15.