Question

Write the next two terms of the A.P. 1, -2, -5….

Answer 1

Hint: Find the first term and the common difference of the A.P. Find the fourth and fifth of the series using the basic formula of arithmetic progression and complete the series.

Complete step-by-step answer:

We know that arithmetic progression is a sequence of numbers such that the difference of any two successive members is a constant. The difference between 2 numbers is called the common difference and is denoted as ‘d’.
We have been given the series 1, -2, -5,….
Let us first find their common difference,
d = 2nd term – 1st term = - 2 - 1 = - 3
d = 3rd term – 1st term = - 5 – (-2) = - 5 + 2 = - 3
Thus we got the common difference = d = - 3.
The first term of the series = 1 = \[{{a}_{1}}\].
We have been given the first 3 terms of the series and we need to find the fourth and the fifth term of the series.
Thus to get the next term of the series, we can use the formula,
\[{{a}_{n}}={{a}_{1}}+(n-1)d\], where \[{{a}_{n}}\] is the \[{{n}^{th}}\] term of the sequence.
Thus let us find the 4th term of the series.
Here \[{{a}_{1}}=1,n-4,d=-3\].
\[\therefore {{a}_{4}}=1+(4-1)(-3)=1+(3\times -3)-1-9=-8\].
Thus the 4th term of the A.P., \[{{a}_{4}}=-8\].
Now, let us find the 5th term of the series,
\[{{a}_{1}}=1,n=5,d=-3\]
\[{{a}_{5}}=1+(5-1)(-3)=1+(4\times -3)=1-12=-11\].
The 5th term of the A.P., \[{{a}_{5}}=-11.\]
So we found the next two terms of A.P. as -8 and -11. Thus the series becomes 1, -2, -5, -8, -11.

Note:Here it is said that the given series is an A.P. but you should be able to identify the given series whether it is A.P., G.P. or H.P. if it’s not given and then apply the necessary formula. You should remember the basic formula to calculate the sum of n terms etc.