Question

the first term of an AP is 5 and the common difference is 7 .Find the difference between the 100th term and 137th term of the AP?

Answer 1

Given

⇒First term (a) = 5

⇒Common Difference (d) = 7

To find

⇒T₁₀₀ - T₁₃₇

Formula

⇒Tₙ = a+(n-1)d

Now we write according to question

⇒[ a+(137-1)d]-[a+(100-1)d]

Where a=5 and d = 7 , put the value on formula

⇒[5+136×7]-[5+99×7]

⇒[5+952]-[5+693]

⇒957-698

⇒259

Answer

⇒259

                                                         

More Information

⇒a,b,c are in AP ; 2b = a+c , GP ; b²=ac and HP ; b = (2ac)/(a+c)

⇒AM = (a+b)/2 , G= √(ab) and H = (2ab)/(a+b)

⇒A≥G≥H        In Equality Based

Answer 2

Given :-

• First term of AP (a) = 5
• Comman difference (d ) = 7
• n¹ = 137
• n² = 100

To Find :-

• the difference between the 100th term and 137th term of AP ( ᵃ 137 - ᵃ100 )

Required Answer :-

$\tt \green{An = a + ( n - 1 ) d } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ ➝ \: \tt \green{A137 - A100 } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ ➝ \tt \green{ (a + ( n¹ - 1 ) d )-( a + ( n² - 1 ) d )} \: \: \: \: \: \: \: \: \\ \\➝ \tt \green{ (5 + (137 - 1) 7) -(5 + (100 - 1)7) } \\ \\ ➝ \tt \green{ (5 + (136)7) - (5 + (99)7)} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ ➝ \tt \green{( 5 + 952) - (5 + 693)} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ ➝ \tt \green{ 957 - 698 } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ ➝ \tt \red{259 } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

I hope it helps you ❤️✔️.