Question

find the general term of an AP whose 7 th term is -1 and 16 th term is 17

Answer 1

Step-by-step explanation:

ANSWER:-

We know that:-

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

Now, given that :-

$\sf{a_7 = -1}$

We can also write it as:-

$\sf{a_7=a+6d}$

$\sf{a+6d = -1}$ __________[1]

And also,

$\sf{a_{16}= 17}$

We can say that:-

$\sf{a_{16}= a+15d}$

$\sf{a+15d=17}$___________[2]

Now, subtracting [2] from [1],

$\sf{a+15d-(a+6d)=17-(-1)}$

$\sf{a+15d-a-6d=17+1}$

$\sf{9d=18}$

$\boxed{\sf{d=2}}$

Now also, we need to find a.

So, placing it in [1],

$\sf{a+6d = -1}$

$\sf{a+6(2) = -1}$

$\sf{a+12= -1}$

$\sf{a = -1-12}$

$\boxed{\sf{a= -13}}$

Formulas Used:-

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

• Where a is the first term.
• Where d is common difference
• Where $\sf{a_n }$ is the nth term.

For summing up any Arithmetic Progression, we use:-

$\boxed{\sf{S_n = \dfrac{n}{2}(2a+n-1)d}}$

• Where S is the total sum
• $\sf{S_n }$ is the total sum till the nth term of the series.