Question

14. The 4th term of an arithmetic sequence is 28 and the 15th term is 105.
find the first term (a1) and the common difference (d) of the sequence
a. a,-7, d=4 b. a1=7, d=5 c. a1=7,
d=6
d. a1=7, d=7
​

Answer 1

Answer:

In the given figure ABCD is a rhombus. AC = 6 cm and BD = 16 cm.

a) Find the measure of A.

Step-by-step explanation:

In the given figure ABCD is a rhombus. AC = 6 cm and BD = 16 cm.

a) Find the measure of A.

Answer 2

S O L U T I O N :

$\underline{\bf{Given\::}}$

The 4th term of an arithmetic is 28 & the 15th term is 105.

$\underline{\bf{Explanation\::}}$

As we know that formula of an A.P;

$\boxed{\bf{a_n = a+(n-1)d}}$

• a is the first term.
• d is the common difference.
• n is the term of an A.P.

A/q

$\mapsto\tt{a_4 = 28}$

$\mapsto\tt{a+(4-1)d = 28}$

$\mapsto\tt{a+(3)d = 28}$

$\mapsto\tt{a+3d = 28}$

$\mapsto\tt{a = 28-3d.............(1)}$

&

$\mapsto\tt{a_{15} = 105}$

$\mapsto\tt{a+(15-1)d = 105}$

$\mapsto\tt{a+(14)d = 105}$

$\mapsto\tt{a+14d= 105}$

$\mapsto\tt{28-3d+14d= 105\:\:\:[from(1)]}$

$\mapsto\tt{28+11d= 105}$

$\mapsto\tt{11d= 105-28}$

$\mapsto\tt{11d= 77}$

$\mapsto\tt{d= \cancel{77/11}}$

$\mapsto\bf{d = 7}$

∴ Putting the value of d in equation (1),we get;

$\mapsto\tt{a = 28-3(7)}$

$\mapsto\tt{a = 28-21}$

$\mapsto\bf{a = 7}$

Thus,

The first term & common difference will be 7 & 7 .

Option (d).