Question

What is its 100th term of the sequence 5, 12, 19, 26

Answer 1

a 100 = 698

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Answer 2

GIVEN:

• A.P. = 5, 12, 19, 26

TO FIND:

• What is the 100th term of an A.P. ?

SOLUTION:

We have given the A.P. = 5, 12, 19, 26

• a = 5

Common difference = d2 – d1

➾ 12 – 5 = 7

• d = 7

No. of terms = n = 100

We know that the formula for finding the nth term of an A.P. is:-

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

According to question:-

On putting the given values in the formula, we get

$\rm{\dashrightarrow a_n = 5 + (100-1)7 }$

$\rm{\dashrightarrow a_n = 5 + 99 \times 7}$

$\rm{\dashrightarrow a_n = 5 + 693 }$

$\bf{\dashrightarrow a_n = 698 }$

❝ Hence, the nth term of an A.P. is 698 ❞

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✯ Extra Information ✯

⇛Sum of n terms = Sn = n/2 [2a + (n–1)d]

⇛ Sum of n terms = Sn = n/2 [a + an]