Question

I don't like maths. ​

Answer 1

Answer :

1. t1 = -11
2. d = 3
3. t4 = 40
4. tn = 21

Explanation:

=>series of an A.P is -11,-8,-5,..., 49

• 1st term = -11

• 2nd term = -8

• last term = -11

• Common difference:

= -8 - (-11)

= -8 + 11

= 3

=>nth term is :

Tn = a+(n-1)d

49 = -11 +(n-1)3

49 = -11 + 3n -3

49 = -14 + 3n

63 = 3n

n = 21

nth term is 21...!!!

=>4th Term from last is :

= l - ( n-1)d

= 49 - ( 4-1)3

= 49 - 9

= 40

Answer 2

So here we have been given with an A.P. (Arithmetic progression) :

• A.P. = -11 , -8 , -5 ,...., 49

But the given A.P. is reversed. So the new A.P. would be,

• 49 , .... , -5 , -8 , -11

★ For first term (a) of the A.P. :

Here by noticing the A.P. we clearly got to know that first term (a) is -11.

★ For common difference (d) :

$: \: \implies \: \sf{ d \: = \: - 8 - ( - 11)}$

$: \: \implies \: \sf{ d \: = \: - 8 \: + \: 11}$

$: \: \implies \: \boxed{\sf{ d \: = \: 3}} \: \red\bigstar$

★ Formula :

Now, we know that general term i.e. nth term of the A.P. is calculated by the formula :

• $\boxed{\bf{t_{n} \: = \: a \: + \: (n - 1) \: d}} \: \red\bigstar$

Here in this formula,

• a id is first term
• d is common difference
• n is number of terms
• tn is the nth term of the A.P.

★ For fourth term of the A.P. (t_4) :

$: \: \implies \: \sf{t_{4} \: = \: 49 \: + \: (4 - 1) \: \times \: ( - 3) }$

$: \: \implies \: \sf{t_{4} \: = \: 49 \: + \: (3) \: \times \: ( - 3) }$

$: \: \implies \: \sf{t_{4} \: = \: 49 \: - \: 9 }$

$: \: \implies \: \boxed{\sf{t_{4} \: = \: 40 }} \: \red\bigstar$

Additional Information :

• Arithmetic progression (A.P.) is a sequence in which each term can be found by adding a certain quantity to its preceding term
• Difference between two consecutive terms is called common difference
• Progression means it's a type of sequence in which each term is related to its predecessor and successor.